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Algebra Universalis最新文献

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On the structure of modal and tense operators on a boolean algebra 布尔代数上模态算子和时态算子的结构
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-04-04 DOI: 10.1007/s00012-025-00890-y
Guram Bezhanishvili, Andre Kornell
{"title":"On the structure of modal and tense operators on a boolean algebra","authors":"Guram Bezhanishvili,&nbsp;Andre Kornell","doi":"10.1007/s00012-025-00890-y","DOIUrl":"10.1007/s00012-025-00890-y","url":null,"abstract":"<div><p>We initiate the study of the poset <span>(mathcal{N}mathcal{O}(B))</span> of necessity operators on a boolean algebra <i>B</i>. We show that <span>(mathcal{N}mathcal{O}(B))</span> is a meet-semilattice that need not be distributive. However, when <i>B</i> is complete, <span>(mathcal{N}mathcal{O}(B))</span> is necessarily a frame, which is spatial iff <i>B</i> is atomic. In that case, <span>(mathcal{N}mathcal{O}(B))</span> is a locally Stone frame. Dual results hold for the poset <span>(mathcal{P}mathcal{O}(B))</span> of possibility operators. We also obtain similar results for the posets <span>(mathcal {TNO}(B))</span> and <span>(mathcal {TPO}(B))</span> of tense necessity and possibility operators on <i>B</i>. Our main tool is Jónsson-Tarski duality, by which such operators correspond to continuous and interior relations on the Stone space of <i>B</i>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143778068","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
Monadic ortholattices: completions and duality 一元正正交：补全和对偶性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-04-03 DOI: 10.1007/s00012-025-00889-5
John Harding, Joseph McDonald, Miguel Peinado
{"title":"Monadic ortholattices: completions and duality","authors":"John Harding,&nbsp;Joseph McDonald,&nbsp;Miguel Peinado","doi":"10.1007/s00012-025-00889-5","DOIUrl":"10.1007/s00012-025-00889-5","url":null,"abstract":"<div><p>We show that the variety of monadic ortholattices is closed under MacNeille and canonical completions. In each case, the completion of <i>L</i> is obtained by forming an associated dual space <i>X</i> that is a monadic orthoframe. This is a set with an orthogonality relation and an additional binary relation satisfying certain conditions. For the MacNeille completion, <i>X</i> is formed from the non-zero elements of <i>L</i>, and for the canonical completion, <i>X</i> is formed from the proper filters of <i>L</i>. The corresponding completion of <i>L</i> is then obtained as the ortholattice of bi-orthogonally closed subsets of <i>X</i> with an additional operation defined through the binary relation of <i>X</i>. With the introduction of a suitable topology on an orthoframe, as was done by Goldblatt and Bimbó, we obtain a dual adjunction between the categories of monadic ortholattices and monadic orthospaces. A restriction of this dual adjunction provides a dual equivalence.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769776","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
Representable distributive quasi relation algebras 可表示分布拟关系代数
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-04-03 DOI: 10.1007/s00012-025-00884-w
Andrew Craig, Claudette Robinson
{"title":"Representable distributive quasi relation algebras","authors":"Andrew Craig,&nbsp;Claudette Robinson","doi":"10.1007/s00012-025-00884-w","DOIUrl":"10.1007/s00012-025-00884-w","url":null,"abstract":"<div><p>We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Galatos and Jipsen (Algebra Univers 69:1–21, 2013). Our definition uses a construction that starts with a poset. The algebra is concretely constructed as the lattice of upsets of a partially ordered equivalence relation. The key to defining the three negation-like unary operations is to impose certain symmetry requirements on the partial order. Our definition of representable distributive quasi relation algebras is easily seen to be a generalisation of the definition of representable relations algebras by Jónsson and Tarski (AMS 54:89, 1948). We give examples of representable DqRAs and give a necessary condition for an algebra to be finitely representable. We leave open the questions of whether every DqRA is representable, and also whether the class of representable DqRAs forms a variety. Moreover, our definition provides many other opportunities for investigations in the spirit of those carried out for representable relation algebras.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00884-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769833","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
Right-preordered groups from a categorical perspective 从分类的角度看右序群
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-03-25 DOI: 10.1007/s00012-025-00886-8
Maria Manuel Clementino, Andrea Montoli
{"title":"Right-preordered groups from a categorical perspective","authors":"Maria Manuel Clementino,&nbsp;Andrea Montoli","doi":"10.1007/s00012-025-00886-8","DOIUrl":"10.1007/s00012-025-00886-8","url":null,"abstract":"<div><p>We study categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, studying some exactness properties, and showing that it is a quasivariety. We show that, from an algebraic point of view, the category of right-preordered groups shares several properties with the one of monoids. Moreover, we describe split extensions of right-preordered groups, showing in particular that semidirect products of ordered groups always have a natural right-preorder.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698528","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
Reorienting quandle orbits 调整烛台轨道的方向
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-03-25 DOI: 10.1007/s00012-025-00883-x
Lorenzo Traldi
{"title":"Reorienting quandle orbits","authors":"Lorenzo Traldi","doi":"10.1007/s00012-025-00883-x","DOIUrl":"10.1007/s00012-025-00883-x","url":null,"abstract":"<div><p>Motivated by knot theory, it is natural to define the orienta-tion-reversal of a quandle orbit by inverting all the translations given by elements of that orbit. In this short note we observe that this natural notion is unsuited to medial quandles.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00883-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698529","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
Characterizations of U-frames and frames that are finitely a U-frame u型框架和有限u型框架的特征
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-03-25 DOI: 10.1007/s00012-025-00888-6
Batsile Tlharesakgosi
{"title":"Characterizations of U-frames and frames that are finitely a U-frame","authors":"Batsile Tlharesakgosi","doi":"10.1007/s00012-025-00888-6","DOIUrl":"10.1007/s00012-025-00888-6","url":null,"abstract":"<div><p>In this article, we give algebraic characterizations of <i>U</i>-frames in terms of ring-theoretic properties of the ring <span>(mathcal {R}L)</span> of real-valued continuous functions on a completely regular frame <i>L</i>. We show that a frame is a <i>U</i>-frame if and only if it is an <i>F</i>-frame and its Čech–Stone compactification is zero-dimensional. We will also introduce frames that are finitely a <i>U</i>-frame and we will characterize them in terms of ring-theoretic properties in <span>(mathcal {R}L)</span>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00888-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698527","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
Correction: Projectivity in (bounded) commutative integral residuated lattices 修正：（有界）交换积分残差格中的投影
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-01-04 DOI: 10.1007/s00012-024-00879-z
Paolo Aglianò, Sara Ugolini
{"title":"Correction: Projectivity in (bounded) commutative integral residuated lattices","authors":"Paolo Aglianò,&nbsp;Sara Ugolini","doi":"10.1007/s00012-024-00879-z","DOIUrl":"10.1007/s00012-024-00879-z","url":null,"abstract":"","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00879-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925585","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
Algebraic frames in Priestley duality Priestley对偶中的代数框架
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-12-30 DOI: 10.1007/s00012-024-00876-2
Guram Bezhanishvili, Sebastian D. Melzer
{"title":"Algebraic frames in Priestley duality","authors":"Guram Bezhanishvili,&nbsp;Sebastian D. Melzer","doi":"10.1007/s00012-024-00876-2","DOIUrl":"10.1007/s00012-024-00876-2","url":null,"abstract":"<div><p>We characterize Priestley spaces of algebraic, arithmetic, coherent, and Stone frames. As a corollary, we derive the well-known dual equivalences in pointfree topology involving various categories of algebraic frames.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890063","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 finite representation of relation algebra (varvec{1896_{3013}}) 关系代数的有限表示 (varvec{1896_{3013}})
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-12-30 DOI: 10.1007/s00012-024-00881-5
Jeremy F. Alm
{"title":"A finite representation of relation algebra (varvec{1896_{3013}})","authors":"Jeremy F. Alm","doi":"10.1007/s00012-024-00881-5","DOIUrl":"10.1007/s00012-024-00881-5","url":null,"abstract":"<div><p>We give a representation of relation algebra <span>(1896_{3013})</span>, which has symmetric atoms <span>(1')</span>, <i>a</i>, <i>b</i>, <i>c</i>, and <i>d</i>. The sole forbidden diversity cycle is <i>bcd</i>; the atom <i>a</i> is flexible. We give a group representation over <span>(mathbb {Z}/1531mathbb {Z})</span>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890046","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 z-elements of multiplicative lattices 在乘法格的z元素上
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-12-28 DOI: 10.1007/s00012-024-00882-4
Amartya Goswami, Themba Dube
{"title":"On z-elements of multiplicative lattices","authors":"Amartya Goswami,&nbsp;Themba Dube","doi":"10.1007/s00012-024-00882-4","DOIUrl":"10.1007/s00012-024-00882-4","url":null,"abstract":"<div><p>The aim of this paper is to investigate further properties of <i>z</i>-elements in multiplicative lattices. We utilize <i>z</i>-closure operators to extend several properties of <i>z</i>-ideals to <i>z</i>-elements and introduce various distinguished subclasses of <i>z</i>-elements, such as <i>z</i>-prime, <i>z</i>-semiprime, <i>z</i>-primary, <i>z</i>-irreducible, and <i>z</i>-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where <i>z</i>-elements are closed under finite products and a representation of <i>z</i>-elements in terms of <i>z</i>-irreducible elements in <i>z</i>-Noetherian multiplicative lattices.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00882-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890032","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
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