Pub Date : 2020-11-05DOI: 10.14712/1213-7243.2020.019
N. Attila
An algebraic structure is said to be congruence permutable if its arbitrary congruences $alpha$ and $beta$ satisfy the equation $alpha circ beta =beta circ alpha$, where $circ$ denotes the usual composition of binary relations. For an arbitrary $G$-set $X$ with $Gcap X=emptyset$, we define a semigroup $(G,X,0)$ with a zero $0$ ($0notin Gcup X$), and give necessary and sufficient conditions for the congruence permutability of the $G$-set $X$ by the help of the semigroup $(G,X,0)$.
{"title":"On congruence permutable $G$-sets","authors":"N. Attila","doi":"10.14712/1213-7243.2020.019","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.019","url":null,"abstract":"An algebraic structure is said to be congruence permutable if its arbitrary congruences $alpha$ and $beta$ satisfy the equation $alpha circ beta =beta circ alpha$, where $circ$ denotes the usual composition of binary relations. For an arbitrary $G$-set $X$ with $Gcap X=emptyset$, we define a semigroup $(G,X,0)$ with a zero $0$ ($0notin Gcup X$), and give necessary and sufficient conditions for the congruence permutability of the $G$-set $X$ by the help of the semigroup $(G,X,0)$.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"61 1","pages":"139-145"},"PeriodicalIF":0.2,"publicationDate":"2020-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67039346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-15DOI: 10.14712/1213-7243.2020.038
Alevs Dr'apal, M. Kinyon
Let $Q$ be a loop. If $Sleq Q$ is such that $varphi(S) subseteq S$ for each standard generator of $mathrm{Inn}(Q)$, then $S$ does not have to be a normal subloop. In an LC loop the left and middle nucleus coincide and form a normal subloop. The identities of Osborn loops are obtained by applying the idea of nuclear identification, and various connections of Osborn loops to Moufang and CC loops are discussed. Every Osborn loop possesses a normal nucleus, and this nucleus coincides with the left, the right and the middle nucleus. Loops that are both Buchsteiner and Osborn are characterized as loops in which each square is in the nucleus.
{"title":"Normality, nuclear squares and Osborn identities","authors":"Alevs Dr'apal, M. Kinyon","doi":"10.14712/1213-7243.2020.038","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.038","url":null,"abstract":"Let $Q$ be a loop. If $Sleq Q$ is such that $varphi(S) subseteq S$ for each standard generator of $mathrm{Inn}(Q)$, then $S$ does not have to be a normal subloop. In an LC loop the left and middle nucleus coincide and form a normal subloop. The identities of Osborn loops are obtained by applying the idea of nuclear identification, and various connections of Osborn loops to Moufang and CC loops are discussed. Every Osborn loop possesses a normal nucleus, and this nucleus coincides with the left, the right and the middle nucleus. Loops that are both Buchsteiner and Osborn are characterized as loops in which each square is in the nucleus.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43349307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-22DOI: 10.14712/1213-7243.2020.007
Drewnowski Lech
. We discuss various results on the existence of ‘true’ preimages under continuous open maps between F -spaces, F -lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.
{"title":"True preimages of compact or separable sets for functional analysts","authors":"Drewnowski Lech","doi":"10.14712/1213-7243.2020.007","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.007","url":null,"abstract":". We discuss various results on the existence of ‘true’ preimages under continuous open maps between F -spaces, F -lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46735960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-22DOI: 10.14712/1213-7243.2020.006
Hui Shyamal K., Lemence Richard S., Mandal Pradip
. A submanifold M m of a generalized Sasakian-space-form M 2 n +1 ( f 1 , f 2 ,f 3 ) is said to be C -totally real submanifold if ξ ∈ Γ( T ⊥ M ) and ϕX ∈ Γ( T ⊥ M ) for all X ∈ Γ( TM ). In particular, if m = n , then M n is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten–van Kampen connection and Tanaka–Webster connection.
{"title":"Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms","authors":" Hui Shyamal K., Lemence Richard S., Mandal Pradip","doi":"10.14712/1213-7243.2020.006","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.006","url":null,"abstract":". A submanifold M m of a generalized Sasakian-space-form M 2 n +1 ( f 1 , f 2 ,f 3 ) is said to be C -totally real submanifold if ξ ∈ Γ( T ⊥ M ) and ϕX ∈ Γ( T ⊥ M ) for all X ∈ Γ( TM ). In particular, if m = n , then M n is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten–van Kampen connection and Tanaka–Webster connection.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42213741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Let R be a commutative ring with identity and A ( R ) be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of R is defined as the graph SAG( R ) with the vertex set A ( R ) ∗ = A ( R ) { 0 } and two distinct vertices I and J are adjacent if and only if I ∩ Ann( J ) 6 = (0) and J ∩ Ann( I ) 6 = (0). In this paper, the perfectness of SAG( R ) for some classes of rings R is investigated.
{"title":"Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings","authors":"Jalali Mitra, Tehranian Abolfazl, Nikandish Reza, Rasouli Hamid","doi":"10.14712/1213-7243.2020.005","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.005","url":null,"abstract":". Let R be a commutative ring with identity and A ( R ) be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of R is defined as the graph SAG( R ) with the vertex set A ( R ) ∗ = A ( R ) { 0 } and two distinct vertices I and J are adjacent if and only if I ∩ Ann( J ) 6 = (0) and J ∩ Ann( I ) 6 = (0). In this paper, the perfectness of SAG( R ) for some classes of rings R is investigated.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49401581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-22DOI: 10.14712/1213-7243.2020.004
S. Amir, R. Mohammad, Ghaderi Eghbal, Zangeneh Hamzeh
In this paper, we study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X,$ the Lipschitz algebras $Lip_{alpha}(X)$ and $ell ip_{alpha}(X)$ are approximately biflat if and only if $X$ is finite, provided that $0 0.$ We also show that some triangular Banach algebras are not approximately biflat.
{"title":"Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras","authors":"S. Amir, R. Mohammad, Ghaderi Eghbal, Zangeneh Hamzeh","doi":"10.14712/1213-7243.2020.004","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.004","url":null,"abstract":"In this paper, we study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X,$ the Lipschitz algebras $Lip_{alpha}(X)$ and $ell ip_{alpha}(X)$ are approximately biflat if and only if $X$ is finite, provided that $0 0.$ We also show that some triangular Banach algebras are not approximately biflat.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"61 1","pages":"83-92"},"PeriodicalIF":0.2,"publicationDate":"2020-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67039339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-12DOI: 10.14712/1213-7243.2022.013
M. Baillif
We use topological consequences of PFA, MA$_{omega_1}$(S)[S] and PFA(S)[S] proved by other authors to show that normal first countable linearly H-closed spaces with various additionals properties are compact in these models.
{"title":"Three small results on normal first countable linearly H-closed spaces","authors":"M. Baillif","doi":"10.14712/1213-7243.2022.013","DOIUrl":"https://doi.org/10.14712/1213-7243.2022.013","url":null,"abstract":"We use topological consequences of PFA, MA$_{omega_1}$(S)[S] and PFA(S)[S] proved by other authors to show that normal first countable linearly H-closed spaces with various additionals properties are compact in these models.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44688107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-21DOI: 10.14712/1213-7243.2020.002
Sousa Lurdes, T. Walter
Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnkov'a's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by Anghel. Our focus in this paper is on differentiating the order-enriched notion from the ordinary one, mostly in terms of the functor's behaviour with respect to specific weighted (co)limits, and on the presentation of examples, which include functors of general varieties of ordered algebras and special ones, such as ordered vector spaces.
{"title":"Order-enriched solid functors","authors":"Sousa Lurdes, T. Walter","doi":"10.14712/1213-7243.2020.002","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.002","url":null,"abstract":"Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnkov'a's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by Anghel. Our focus in this paper is on differentiating the order-enriched notion from the ordinary one, mostly in terms of the functor's behaviour with respect to specific weighted (co)limits, and on the presentation of examples, which include functors of general varieties of ordered algebras and special ones, such as ordered vector spaces.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":"60 1","pages":"553-580"},"PeriodicalIF":0.2,"publicationDate":"2020-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67039296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-21DOI: 10.14712/1213-7243.2019.029
Levy Paul B.
. We show that, on a category of many-sorted sets, the only functors that admit a cartesian strength are those that are given componentwise.
.我们证明，在许多排序集的范畴上，唯一允许笛卡尔强度的函子是那些按分量给定的函子。
{"title":"Strong functors on many-sorted sets","authors":" Levy Paul B.","doi":"10.14712/1213-7243.2019.029","DOIUrl":"https://doi.org/10.14712/1213-7243.2019.029","url":null,"abstract":". We show that, on a category of many-sorted sets, the only functors that admit a cartesian strength are those that are given componentwise.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45584587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-08DOI: 10.14712/1213-7243.2021.008
A. Azizi, M. M. Chems-Eddin, A. Zekhnini
Let $d$ be a square free integer and $L_d:=mathbb{Q}(zeta_{8},sqrt{d})$. In the present work we determine all the fields $L_d$ such that the $2$-class group, $mathrm{Cl}_2(L_d)$, of $L_d$ is of type $(2,4)$ or $(2,2,2)$.
{"title":"On some imaginary triquadratic number fields $k$ with ${rm Cl}_2(k) simeq (2, 4)$ or $(2, 2, 2)$","authors":"A. Azizi, M. M. Chems-Eddin, A. Zekhnini","doi":"10.14712/1213-7243.2021.008","DOIUrl":"https://doi.org/10.14712/1213-7243.2021.008","url":null,"abstract":"Let $d$ be a square free integer and $L_d:=mathbb{Q}(zeta_{8},sqrt{d})$. In the present work we determine all the fields $L_d$ such that the $2$-class group, $mathrm{Cl}_2(L_d)$, of $L_d$ is of type $(2,4)$ or $(2,2,2)$.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47781586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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