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Algebra Universalis最新文献

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Joins and meets in effect algebras 效应代数中的连接和相遇
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-03-01 DOI: 10.1007/s00012-024-00844-w
Grzegorz Bińczak, Joanna Kaleta, Andrzej Zembrzuski
{"title":"Joins and meets in effect algebras","authors":"Grzegorz Bińczak,&nbsp;Joanna Kaleta,&nbsp;Andrzej Zembrzuski","doi":"10.1007/s00012-024-00844-w","DOIUrl":"10.1007/s00012-024-00844-w","url":null,"abstract":"<div><p>It is known that every effect algebra can be represented as the effect algebra of perspectivity classes of some <i>E</i>-test space. We describe when there exists join and meet of two perspectivity classes of events of some algebraic <i>E</i>-test space. Moreover we give the formula for join and meet of perspectivity classes mentioned above, using only tests. We obtain an example of finite, non-homogeneous effect algebra <i>E</i> such that sharp elements of <i>E</i> form a lattice, whereas <i>E</i> is not a lattice.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00844-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140017896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hull classes in compact regular frames 紧凑正则框架中的船体类
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-03-01 DOI: 10.1007/s00012-024-00849-5
Papiya Bhattacharjee, Ricardo E. Carrera
{"title":"Hull classes in compact regular frames","authors":"Papiya Bhattacharjee,&nbsp;Ricardo E. Carrera","doi":"10.1007/s00012-024-00849-5","DOIUrl":"10.1007/s00012-024-00849-5","url":null,"abstract":"<div><p><span>(mathfrak {KReg})</span> is the category of compact regular frames and frame homomorphisms. A class of <span>(mathfrak {KReg})</span> frames <span>(textbf{H})</span> is a hull class provided that: (i) <span>(textbf{H})</span> is closed under isomorphic copies; (ii) for every <span>(F in mathfrak {KReg})</span> there exist an <span>(hF in textbf{H})</span> and a morphism <span>(h_F)</span> such that <span>(F overset{h_F}{le } hF)</span> is essential; (iii) if <span>(F overset{phi }{le } H)</span> is essential and <span>(H in textbf{H})</span>, then there exists <span>(hphi : hF longrightarrow H)</span> for which <span>(phi = hphi cdot h_F)</span>. This work provides techniques for identifying and generating hull classes in <span>(mathfrak {KReg})</span>. Moreover, for a compact regular frame <i>F</i>, we introduce and investigate various properties of projectability and disconnectivity of <i>F</i> and prove that for each property, <i>P</i>, the class of <span>(mathfrak {KReg})</span>-objects that satisfy <i>P</i> is a hull class in <span>(mathfrak {KReg})</span>. In addition, we provide examples of <span>(mathfrak {KReg})</span> hull classes that are not characterized by some form of projectability/disconnectivity and examples of classes of <span>(mathfrak {KReg})</span>-objects that are not hull classes.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00849-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140017801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solution to two problems on ideally conjunctive join-semilattices 关于理想结合接合-半方阵的两个问题的解答
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-02-22 DOI: 10.1007/s00012-024-00845-9
Ao Shen, Qingguo Li
{"title":"Solution to two problems on ideally conjunctive join-semilattices","authors":"Ao Shen,&nbsp;Qingguo Li","doi":"10.1007/s00012-024-00845-9","DOIUrl":"10.1007/s00012-024-00845-9","url":null,"abstract":"<div><p>In this paper, we solve two problems concerning the ideally conjunctive join-semilattices. First, we show that <span>(L/R^1({{,textrm{Id},}}L)|_L)</span> is ideally conjunctive for all join-semilattices <i>L</i>. Then we characterize those ideally conjunctive join-semilattices <i>L</i> such that <span>({{,textrm{coz},}}a)</span> is compact for all <span>(ain L.)</span> Moreover, we give the definition of conjunctive posets and prove that the category of ideally conjunctive join-semilattices and join homomorphisms is reflective in the category of conjunctive posets and weakly ideal-continuous maps. As a corollary, we obtain the free ideally conjunctive join-semilattices over conjunctive posets.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139919537","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
On the Boolean algebra induced by a unital (ell )-group 论由单元 $$ell $$ - 群诱导的布尔代数
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-02-22 DOI: 10.1007/s00012-024-00848-6
Soudabeh Karamdoust, Hassan Myrnouri, Mahmood Pourgholamhossein
{"title":"On the Boolean algebra induced by a unital (ell )-group","authors":"Soudabeh Karamdoust,&nbsp;Hassan Myrnouri,&nbsp;Mahmood Pourgholamhossein","doi":"10.1007/s00012-024-00848-6","DOIUrl":"10.1007/s00012-024-00848-6","url":null,"abstract":"<div><p>The main goal of this paper is the study of the Boolean algebra of all characteristic elements in a unital <span>(ell )</span>-group and we investigate some topological properties of it in the case that the unital <span>(ell )</span>-group equipped with a link or positive filter topology. We also introduce the concept of Boolean region as a subset of a unital <span>(ell )</span>-group.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00848-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139919406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Was Ulam right? II: small width and general ideals 乌兰说得对吗？二：小范围和一般理想
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-02-17 DOI: 10.1007/s00012-024-00843-x
Tanmay Inamdar, Assaf Rinot
{"title":"Was Ulam right? II: small width and general ideals","authors":"Tanmay Inamdar,&nbsp;Assaf Rinot","doi":"10.1007/s00012-024-00843-x","DOIUrl":"10.1007/s00012-024-00843-x","url":null,"abstract":"<div><p>We continue our study of Sierpiński-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension by Hajnal, it is proved that if <span>(kappa )</span> is a regular uncountable cardinal that is not weakly compact in <i>L</i>, then there is a universal witness for non-weak-saturation of <span>(kappa )</span>-complete ideals. Specifically, there are <span>(kappa )</span>-many decompositions of <span>(kappa )</span> such that, for every <span>(kappa )</span>-complete ideal <i>J</i> over <span>(kappa )</span>, and every <span>(Bin J^+)</span>, one of the decompositions shatters <i>B</i> into <span>(kappa )</span>-many <span>(J^+)</span>-sets. A second focus here is the feature of narrowness of colourings, one already present in the theorem of Sierpiński. This feature ensures that a colouring suitable for an ideal is also suitable for all superideals possessing the requisite completeness degree. It is proved that unlike successors of regulars, every successor of a singular cardinal admits such a narrow colouring.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00843-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Not all nilpotent monoids are finitely related 并非所有零势单元都是有限相关的
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-02-14 DOI: 10.1007/s00012-023-00841-5
Markus Steindl
{"title":"Not all nilpotent monoids are finitely related","authors":"Markus Steindl","doi":"10.1007/s00012-023-00841-5","DOIUrl":"10.1007/s00012-023-00841-5","url":null,"abstract":"<div><p>A finite semigroup is finitely related (has finite degree) if its term functions are determined by a finite set of finitary relations. For example, it is known that all nilpotent semigroups are finitely related. A nilpotent monoid is a nilpotent semigroup with adjoined identity. We show that every 4-nilpotent monoid is finitely related. We also give an example of a 5-nilpotent monoid that is not finitely related. To our knowledge, this is the first example of a finitely related semigroup where adjoining an identity yields a semigroup which is not finitely related. We also provide examples of finitely related semigroups which have subsemigroups, homomorphic images, and in particular Rees quotients, that are not finitely related.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00841-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bubble lattices I: Structure 气泡网格 I：结构
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-02-07 DOI: 10.1007/s00012-024-00842-y
Thomas McConville, Henri Mühle
{"title":"Bubble lattices I: Structure","authors":"Thomas McConville,&nbsp;Henri Mühle","doi":"10.1007/s00012-024-00842-y","DOIUrl":"10.1007/s00012-024-00842-y","url":null,"abstract":"<div><p>C. Greene introduced the shuffle lattice as an idealized model for DNA mutation and discovered remarkable combinatorial and enumerative properties of this structure. We attempt an explanation of these properties from a lattice-theoretic point of view. To that end, we introduce and study an order extension of the shuffle lattice, the <i>bubble lattice</i>. We characterize the bubble lattice both locally (via certain transformations of shuffle words) and globally (using a notion of inversion set). We then prove that the bubble lattice is extremal and constructable by interval doublings. Lastly, we prove that our bubble lattice is a generalization of the Hochschild lattice studied earlier by Chapoton, Combe and the second author.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762448","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
Finitely based congruence varieties 有限同余变种
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-01-12 DOI: 10.1007/s00012-023-00840-6
Ralph Freese, Paolo Lipparini
{"title":"Finitely based congruence varieties","authors":"Ralph Freese,&nbsp;Paolo Lipparini","doi":"10.1007/s00012-023-00840-6","DOIUrl":"10.1007/s00012-023-00840-6","url":null,"abstract":"<div><p>We show that for a large class of varieties of algebras, the equational theory of the congruence lattices of the members is not finitely based.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139458712","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
Semilinear De Morgan monoids and epimorphisms 半线性德摩根单体和外延
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-01-09 DOI: 10.1007/s00012-023-00837-1
J. J. Wannenburg, J. G. Raftery
{"title":"Semilinear De Morgan monoids and epimorphisms","authors":"J. J. Wannenburg,&nbsp;J. G. Raftery","doi":"10.1007/s00012-023-00837-1","DOIUrl":"10.1007/s00012-023-00837-1","url":null,"abstract":"<div><p>A representation theorem is proved for De Morgan monoids that are (i) <i>semilinear</i>, i.e., subdirect products of totally ordered algebras, and (ii) <i>negatively generated</i>, i.e., generated by lower bounds of the neutral element. Using this theorem, we prove that the De Morgan monoids satisfying (i) and (ii) form a variety—in fact, a locally finite variety. We then prove that epimorphisms are surjective in every variety of negatively generated semilinear De Morgan monoids. In the process, epimorphism-surjectivity is established for several other classes as well, including the variety of all semilinear idempotent commutative residuated lattices and all varieties of negatively generated semilinear Dunn monoids. The results settle natural questions about Beth-style definability for a range of substructural logics.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00837-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139414180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Priestley-style duality for DN-algebras DN 矩阵的普里斯特利式对偶性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-01-03 DOI: 10.1007/s00012-023-00838-0
Luciano J. González
{"title":"Priestley-style duality for DN-algebras","authors":"Luciano J. González","doi":"10.1007/s00012-023-00838-0","DOIUrl":"10.1007/s00012-023-00838-0","url":null,"abstract":"<div><p>The aim of this article is to develop a Priestley-style duality for the variety of DN-algebras. In order to achieve this, we use the concept of free distributive lattice extension of a DN-algebra. We establish a connection with the Priestley duality for distributive lattices. Finally, we present topological descriptions for the lattice of filters, for the lattice of congruences, and for certain kinds of subalgebras of a DN-algebra.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139102009","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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