Pub Date : 2023-11-06DOI: 10.1007/s11083-023-09651-9
Mauricio Medina-Bárcenas, Hugo Rincón Mejía
Abstract In this paper we introduce the notions of Rickart and Baer lattices and their duals. We show that part of the theory of Rickart and Baer modules can be understood just using techniques from the theory of lattices. For, we use linear morphisms introduced by T. Albu and M. Iosif. We focus on a submonoid with zero $$mathfrak {m}$$ m of the monoid of all linear endomorphism of a lattice $$mathcal {L}$$ L in order to give a more general approach and apply our results in the theory of modules. We also show that $$mathfrak {m}$$ m -Rickart and $$mathfrak {m}$$ m -Baer lattices can be characterized by the annihilators in $$mathfrak {m}$$ m generated by idempotents as in the case of modules.
摘要本文介绍了ricart格和Baer格及其对偶的概念。我们证明了ricart和Baer模块的部分理论可以用格理论中的技术来理解。因为，我们使用了T. Albu和M. Iosif引入的线性态射。为了给出一个更一般的方法并将我们的结果应用于模的理论，我们重点研究了一个格的所有线性自同态的模$$mathcal {L}$$ L的一个0 $$mathfrak {m}$$ m的子模。我们还证明了$$mathfrak {m}$$ m -Rickart和$$mathfrak {m}$$ m -Baer晶格可以用$$mathfrak {m}$$ m中由模的幂等产生的湮灭子来表征。
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Pub Date : 2023-10-28DOI: 10.1007/s11083-023-09649-3
Gergő Gyenizse, Péter Hajnal, László Zádori
{"title":"Representations of Finite Groups by Posets of Small Height","authors":"Gergő Gyenizse, Péter Hajnal, László Zádori","doi":"10.1007/s11083-023-09649-3","DOIUrl":"https://doi.org/10.1007/s11083-023-09649-3","url":null,"abstract":"","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136159671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-27DOI: 10.1007/s11083-023-09648-4
Jani Jokela
Abstract A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and semigroups, while the more general notion of a mixed lattice remains unexplored. In this paper, we study the fundamental properties of mixed lattices and the relationships between the various properties. In particular, we establish the equivalence of the one-sided associative, distributive and modular laws in mixed lattices. We also give an alternative definition of mixed lattices and mixed lattice groups as non-commutative and non-associative algebras satisfying a certain set of postulates. The algebraic and the order-theoretic definitions are then shown to be equivalent.
{"title":"General Mixed Lattices","authors":"Jani Jokela","doi":"10.1007/s11083-023-09648-4","DOIUrl":"https://doi.org/10.1007/s11083-023-09648-4","url":null,"abstract":"Abstract A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and semigroups, while the more general notion of a mixed lattice remains unexplored. In this paper, we study the fundamental properties of mixed lattices and the relationships between the various properties. In particular, we establish the equivalence of the one-sided associative, distributive and modular laws in mixed lattices. We also give an alternative definition of mixed lattices and mixed lattice groups as non-commutative and non-associative algebras satisfying a certain set of postulates. The algebraic and the order-theoretic definitions are then shown to be equivalent.","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135537813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A short note on the characterization of countable chains with finite big Ramsey spectra","authors":"Keegan Dasilva Barbosa, Dragan Mašulović, Rajko Nenadov","doi":"10.1007/s11083-023-09647-5","DOIUrl":"https://doi.org/10.1007/s11083-023-09647-5","url":null,"abstract":"","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135939192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-08DOI: 10.1007/s11083-023-09641-x
Jérémie Dusart, M. Habib, D. Corneil
{"title":"Maximal Cliques Lattices Structures for Cocomparability Graphs with Algorithmic Applications","authors":"Jérémie Dusart, M. Habib, D. Corneil","doi":"10.1007/s11083-023-09641-x","DOIUrl":"https://doi.org/10.1007/s11083-023-09641-x","url":null,"abstract":"","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43570718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-03DOI: 10.1007/s11083-023-09645-7
Xia Zhang, V. Laan, Jianjun Feng
{"title":"Injective Hulls are Completions of Ordered Algebras","authors":"Xia Zhang, V. Laan, Jianjun Feng","doi":"10.1007/s11083-023-09645-7","DOIUrl":"https://doi.org/10.1007/s11083-023-09645-7","url":null,"abstract":"","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48223265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-17DOI: 10.1007/s11083-023-09638-6
D. Georgiou, A. Megaritis, G. Prinos, F. Sereti
{"title":"A Study of the Small Inductive Dimension in the Area of Finite Lattices","authors":"D. Georgiou, A. Megaritis, G. Prinos, F. Sereti","doi":"10.1007/s11083-023-09638-6","DOIUrl":"https://doi.org/10.1007/s11083-023-09638-6","url":null,"abstract":"","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48055813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-14DOI: 10.1007/s11083-023-09640-y
M. Dugas, D. Herden
{"title":"The Dedekind-MacNeille Completion of a Poset as a Set of Ideals of the Incidence Algebra","authors":"M. Dugas, D. Herden","doi":"10.1007/s11083-023-09640-y","DOIUrl":"https://doi.org/10.1007/s11083-023-09640-y","url":null,"abstract":"","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45594387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-13DOI: 10.1007/s11083-023-09639-5
Koyo Hayashi, Hiroshi Hirai
{"title":"Two Flags in a Semimodular Lattice Generate an Antimatroid","authors":"Koyo Hayashi, Hiroshi Hirai","doi":"10.1007/s11083-023-09639-5","DOIUrl":"https://doi.org/10.1007/s11083-023-09639-5","url":null,"abstract":"","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136101879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.1007/s11083-023-09631-z
Júnio Luan Pereira
{"title":"Weakenings of the Knaster property","authors":"Júnio Luan Pereira","doi":"10.1007/s11083-023-09631-z","DOIUrl":"https://doi.org/10.1007/s11083-023-09631-z","url":null,"abstract":"","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49235877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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