Pub Date : 2023-12-11DOI: 10.1007/s00233-023-10401-x
Żywilla Fechner, Eszter Gselmann, László Székelyhidi
We consider moment functions of higher order. In our earlier paper, we have already investigated the moment functions of higher order on groups. The main purpose of this work is to prove characterization theorems for moment functions on the multivariate polynomial hypergroups and on the Sturm–Liouville hypergroups. In the first case, the moment generating functions of higher rank are partial derivatives (taken at zero) of the composition of generating polynomials of the hypergroup and functions whose coordinates are given by the formal power series. On Sturm–Liouville hypergroups the moment functions of higher rank are restrictions of even smooth functions that also satisfy certain boundary value problems. The second characterization of moment functions of higher rank on Sturm–Liouville hypergroups is given by means of an exponential family. In this case, the moment functions of higher rank are partial derivatives of an appropriately modified exponential family again taken at zero.
{"title":"Moment functions of higher rank on some types of hypergroups","authors":"Żywilla Fechner, Eszter Gselmann, László Székelyhidi","doi":"10.1007/s00233-023-10401-x","DOIUrl":"https://doi.org/10.1007/s00233-023-10401-x","url":null,"abstract":"<p>We consider moment functions of higher order. In our earlier paper, we have already investigated the moment functions of higher order on groups. The main purpose of this work is to prove characterization theorems for moment functions on the multivariate polynomial hypergroups and on the Sturm–Liouville hypergroups. In the first case, the moment generating functions of higher rank are partial derivatives (taken at zero) of the composition of generating polynomials of the hypergroup and functions whose coordinates are given by the formal power series. On Sturm–Liouville hypergroups the moment functions of higher rank are restrictions of even smooth functions that also satisfy certain boundary value problems. The second characterization of moment functions of higher rank on Sturm–Liouville hypergroups is given by means of an exponential family. In this case, the moment functions of higher rank are partial derivatives of an appropriately modified exponential family again taken at zero.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"83 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138572633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-04DOI: 10.1007/s00233-023-10400-y
Alexander V. Osipov, Konstantin Kazachenko
We study the separately continuous actions of semitopological monoids on pseudocompact spaces. The main aim of this paper is to generalize Lawson’s results to some class of pseudocompact spaces. Also, we introduce the concept of a weak (q_D)-space and prove that a pseudocompact space and a weak (q_D)-space form a Grothendieck pair. As an application of the main result, we investigate the continuity of multiplication and taking inverses in subgroups of semitopological semigroups. In particular, we get that if ((S, bullet )) is a Tychonoff pseudocompact semitopological monoid with a quasicontinuous multiplication (bullet ) and G is a subgroup of S, then G is a topological group. Also, we study the continuity of operations in semitopological semilattices.
{"title":"Joint continuity in semitopological monoids and semilattices","authors":"Alexander V. Osipov, Konstantin Kazachenko","doi":"10.1007/s00233-023-10400-y","DOIUrl":"https://doi.org/10.1007/s00233-023-10400-y","url":null,"abstract":"<p>We study the separately continuous actions of semitopological monoids on pseudocompact spaces. The main aim of this paper is to generalize Lawson’s results to some class of pseudocompact spaces. Also, we introduce the concept of a weak <span>(q_D)</span>-space and prove that a pseudocompact space and a weak <span>(q_D)</span>-space form a Grothendieck pair. As an application of the main result, we investigate the continuity of multiplication and taking inverses in subgroups of semitopological semigroups. In particular, we get that if <span>((S, bullet ))</span> is a Tychonoff pseudocompact semitopological monoid with a quasicontinuous multiplication <span>(bullet )</span> and <i>G</i> is a subgroup of <i>S</i>, then <i>G</i> is a topological group. Also, we study the continuity of operations in semitopological semilattices.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":" 12","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138493886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-04DOI: 10.1007/s00233-023-10399-2
Olga B. Sapir
Jackson and Lee proved that certain six-element monoid generates a hereditarily finitely based variety ({{mathbb {E}}}^1) whose lattice of subvarieties contains an infinite ascending chain. We identify syntactic monoids which generate finitely generated subvarieties of ({{mathbb {E}}}^1) and show that one of these finite monoids together with certain seven-element monoid generates a new limit variety.
{"title":"Limit varieties generated by finite non-J-trivial aperiodic monoids","authors":"Olga B. Sapir","doi":"10.1007/s00233-023-10399-2","DOIUrl":"https://doi.org/10.1007/s00233-023-10399-2","url":null,"abstract":"<p>Jackson and Lee proved that certain six-element monoid generates a hereditarily finitely based variety <span>({{mathbb {E}}}^1)</span> whose lattice of subvarieties contains an infinite ascending chain. We identify syntactic monoids which generate finitely generated subvarieties of <span>({{mathbb {E}}}^1)</span> and show that one of these finite monoids together with certain seven-element monoid generates a new limit variety.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":" 11","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138493887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1007/s00233-023-10394-7
Xavier Mary
{"title":"On the structure of semigroups whose regular elements are completely regular","authors":"Xavier Mary","doi":"10.1007/s00233-023-10394-7","DOIUrl":"https://doi.org/10.1007/s00233-023-10394-7","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":" 25","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1007/s00233-023-10390-x
Gracinda M. S. Gomes, Ana-Catarina C. Monteiro
{"title":"Formations of orthodox semigroups","authors":"Gracinda M. S. Gomes, Ana-Catarina C. Monteiro","doi":"10.1007/s00233-023-10390-x","DOIUrl":"https://doi.org/10.1007/s00233-023-10390-x","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":" 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1007/s00233-023-10395-6
Sin-Ei Takahasi
{"title":"Homeomorphism groups on the positive real numbers defined by binary operations","authors":"Sin-Ei Takahasi","doi":"10.1007/s00233-023-10395-6","DOIUrl":"https://doi.org/10.1007/s00233-023-10395-6","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":" 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1007/s00233-023-10397-4
Peter M. Higgins, Marcel Jackson
Abstract We apply, in the context of semigroups, the main theorem from the authors’ paper “Algebras defined by equations” (Higgins and Jackson in J Algebra 555:131–156, 2020) that an elementary class $${mathscr {C}}$$ C of algebras which is closed under the taking of direct products and homomorphic images is defined by systems of equations. We prove a dual to the Birkhoff theorem in that if the class is also closed under the taking of containing semigroups, some basis of equations of $${mathscr {C}}$$ C is free of the $$forall $$ ∀ quantifier. We also observe the decidability of the class of equation systems satisfied by semigroups, via a link to systems of rationally constrained equations on free semigroups. Examples are given of EHP-classes for which neither $$(forall cdots )(exists cdots )$$ (∀⋯)(∃⋯) equation systems nor $$(exists cdots )(forall cdots )$$ (∃⋯)(∀⋯) systems suffice.
{"title":"Equationally defined classes of semigroups","authors":"Peter M. Higgins, Marcel Jackson","doi":"10.1007/s00233-023-10397-4","DOIUrl":"https://doi.org/10.1007/s00233-023-10397-4","url":null,"abstract":"Abstract We apply, in the context of semigroups, the main theorem from the authors’ paper “Algebras defined by equations” (Higgins and Jackson in J Algebra 555:131–156, 2020) that an elementary class $${mathscr {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> of algebras which is closed under the taking of direct products and homomorphic images is defined by systems of equations. We prove a dual to the Birkhoff theorem in that if the class is also closed under the taking of containing semigroups, some basis of equations of $${mathscr {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> is free of the $$forall $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>∀</mml:mo> </mml:math> quantifier. We also observe the decidability of the class of equation systems satisfied by semigroups, via a link to systems of rationally constrained equations on free semigroups. Examples are given of EHP-classes for which neither $$(forall cdots )(exists cdots )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>∀</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>)</mml:mo> <mml:mo>(</mml:mo> <mml:mo>∃</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> equation systems nor $$(exists cdots )(forall cdots )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>∃</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>)</mml:mo> <mml:mo>(</mml:mo> <mml:mo>∀</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> systems suffice.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1007/s00233-023-10396-5
Ilinka Dimitrova, Vítor H. Fernandes, Jörg Koppitz, Teresa M. Quinteiro
{"title":"Presentations for three remarkable submonoids of the dihedral inverse monoid on a finite set","authors":"Ilinka Dimitrova, Vítor H. Fernandes, Jörg Koppitz, Teresa M. Quinteiro","doi":"10.1007/s00233-023-10396-5","DOIUrl":"https://doi.org/10.1007/s00233-023-10396-5","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"300 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135808250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.1007/s00233-023-10393-8
George Fikioris, Giannis Fikioris
Abstract A recent paper studied an inverse submonoid $$M_{n}$$ Mn of the rook monoid, by representing the nonzero elements of $$M_{n}$$ Mn via certain triplets belonging to $${mathbb {Z}}^3$$ Z3 . In this note, we allow the triplets to belong to $${mathbb {R}}^3$$ R3 . We thus study a new inverse monoid $$overline{M}_{n}$$ M¯n , which is a supermonoid of $$M_{n}$$ Mn . We point out similarities and find essential differences. We show that $$overline{M}_{n}$$ M¯n is a noncommutative, periodic, combinatorial, fundamental, completely semisimple, and strongly $${E}^{*}$$ E∗ -unitary inverse monoid.
摘要本文研究了车单阵的一个逆子单阵$$M_{n}$$ mn，通过若干属于$${mathbb {Z}}^3$$ z3的三元组来表示$$M_{n}$$ mn的非零元素。在本文中，我们允许三元组属于$${mathbb {R}}^3$$ r3。因此，我们研究了一个新的逆单阵$$overline{M}_{n}$$ M¯n，它是$$M_{n}$$ M n的超单阵。我们指出相似之处，找出本质的不同之处。我们证明$$overline{M}_{n}$$ M¯n是一个非交换的、周期的、组合的、基本的、完全半简单的、强的$${E}^{*}$$ E * -酉逆单群。
{"title":"An extension to “A subsemigroup of the rook monoid”","authors":"George Fikioris, Giannis Fikioris","doi":"10.1007/s00233-023-10393-8","DOIUrl":"https://doi.org/10.1007/s00233-023-10393-8","url":null,"abstract":"Abstract A recent paper studied an inverse submonoid $$M_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> of the rook monoid, by representing the nonzero elements of $$M_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> via certain triplets belonging to $${mathbb {Z}}^3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> . In this note, we allow the triplets to belong to $${mathbb {R}}^3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> . We thus study a new inverse monoid $$overline{M}_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mover> <mml:mi>M</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>n</mml:mi> </mml:msub> </mml:math> , which is a supermonoid of $$M_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> . We point out similarities and find essential differences. We show that $$overline{M}_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mover> <mml:mi>M</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>n</mml:mi> </mml:msub> </mml:math> is a noncommutative, periodic, combinatorial, fundamental, completely semisimple, and strongly $${E}^{*}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:math> -unitary inverse monoid.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135728952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-17DOI: 10.1007/s00233-023-10392-9
Becky Armstrong, Jonathan H. Brown, Lisa Orloff Clark, Kristin Courtney, Ying-Fen Lin, Kathryn McCormick, Jacqui Ramagge
Abstract In this note, we present criteria that are equivalent to a locally compact Hausdorff groupoid G being effective. One of these conditions is that G satisfies the C*-algebraic local bisection hypothesis ; that is, that every normaliser in the reduced twisted groupoid C*-algebra is supported on an open bisection. The semigroup of normalisers plays a fundamental role in our proof, as does the semigroup of normalisers in cyclic group C*-algebras.
{"title":"The local bisection hypothesis for twisted groupoid C*-algebras","authors":"Becky Armstrong, Jonathan H. Brown, Lisa Orloff Clark, Kristin Courtney, Ying-Fen Lin, Kathryn McCormick, Jacqui Ramagge","doi":"10.1007/s00233-023-10392-9","DOIUrl":"https://doi.org/10.1007/s00233-023-10392-9","url":null,"abstract":"Abstract In this note, we present criteria that are equivalent to a locally compact Hausdorff groupoid G being effective. One of these conditions is that G satisfies the C*-algebraic local bisection hypothesis ; that is, that every normaliser in the reduced twisted groupoid C*-algebra is supported on an open bisection. The semigroup of normalisers plays a fundamental role in our proof, as does the semigroup of normalisers in cyclic group C*-algebras.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号