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$$mathfrak {m}$$-Baer and $$mathfrak {m}$$-Rickart Lattices $$mathfrak {m}$$-Baer和$$mathfrak {m}$$ -Rickart格
4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-11-06 DOI: 10.1007/s11083-023-09651-9
Mauricio Medina-Bárcenas, Hugo Rincón Mejía
{"title":"$$mathfrak {m}$$-Baer and $$mathfrak {m}$$-Rickart Lattices","authors":"Mauricio Medina-Bárcenas, Hugo Rincón Mejía","doi":"10.1007/s11083-023-09651-9","DOIUrl":"https://doi.org/10.1007/s11083-023-09651-9","url":null,"abstract":"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 $$mathfrak {m}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>m</mml:mi> </mml:math> of the monoid of all linear endomorphism of a lattice $$mathcal {L}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>L</mml:mi> </mml:math> in order to give a more general approach and apply our results in the theory of modules. We also show that $$mathfrak {m}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>m</mml:mi> </mml:math> -Rickart and $$mathfrak {m}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>m</mml:mi> </mml:math> -Baer lattices can be characterized by the annihilators in $$mathfrak {m}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>m</mml:mi> </mml:math> generated by idempotents as in the case of modules.","PeriodicalId":54667,"journal":{"name":"Order-A Journal on the Theory of Ordered Sets and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135634037","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}
引用次数: 0
Representations of Finite Groups by Posets of Small Height 用小高度偏序集表示有限群
4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-10-28 DOI: 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}
引用次数: 0
General Mixed Lattices 一般混合格
4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-09-27 DOI: 10.1007/s11083-023-09648-4
Jani Jokela
{"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}
引用次数: 0
A short note on the characterization of countable chains with finite big Ramsey spectra 有限大Ramsey谱的可数链的表征
4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-09-11 DOI: 10.1007/s11083-023-09647-5
Keegan Dasilva Barbosa, Dragan Mašulović, Rajko Nenadov
{"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}
引用次数: 0
Maximal Cliques Lattices Structures for Cocomparability Graphs with Algorithmic Applications 可比较图的极大Cliques格结构及其算法应用
IF 0.4 4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-08-08 DOI: 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}
引用次数: 0
Injective Hulls are Completions of Ordered Algebras 内射壳是有序代数的补全
IF 0.4 4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-08-03 DOI: 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}
引用次数: 0
A Study of the Small Inductive Dimension in the Area of Finite Lattices 有限格区域中的小归纳维数的研究
IF 0.4 4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-06-17 DOI: 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}
引用次数: 0
The Dedekind-MacNeille Completion of a Poset as a Set of Ideals of the Incidence Algebra 作为关联代数的一组理想的Poset的Dedekind-MacNeille完备
IF 0.4 4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-06-14 DOI: 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}
引用次数: 0
Two Flags in a Semimodular Lattice Generate an Antimatroid 半模格上的两个标志生成一个反拟阵
4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-06-13 DOI: 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}
引用次数: 0
Weakenings of the Knaster property Knaster属性的弱化
IF 0.4 4区 数学
Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-06-01 DOI: 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}
引用次数: 0
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