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A note on Cayley-type theorem for distributive lattices 关于分配格的cayley型定理的注解
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-05-05 DOI: 10.1007/s00012-026-00932-z
Bisham Dewan, Arun Kumar
{"title":"A note on Cayley-type theorem for distributive lattices","authors":"Bisham Dewan,&nbsp;Arun Kumar","doi":"10.1007/s00012-026-00932-z","DOIUrl":"10.1007/s00012-026-00932-z","url":null,"abstract":"<div><p>We establish a Cayley-type representation theorem for distributive lattices by constructing an embedding into a suitable endomorphism structure.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147808180","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
Quantum-Wajsberg algebras Quantum-Wajsberg代数
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-05-05 DOI: 10.1007/s00012-026-00921-2
Lavinia Corina Ciungu
{"title":"Quantum-Wajsberg algebras","authors":"Lavinia Corina Ciungu","doi":"10.1007/s00012-026-00921-2","DOIUrl":"10.1007/s00012-026-00921-2","url":null,"abstract":"<div><p>Starting from involutive BE algebras, we redefine the quantum-MV algebras, by introducing and studying the notion of quantum-Wajsberg algebras. We define the <span>(vee )</span>-commutative quantum-Wajsberg algebras and we investigate their properties. We also prove that any Wajsberg algebra is a quantum-Wajsberg algebra, and give conditions for quantum-Wajsberg algebras to be Wajsberg algebras. Furthermore, we prove that Wajsberg algebras are both quantum-Wajsberg algebras and commutative quantum-B algebras. Finally, we provide certain conditions for quantum-MV algebras to be MV algebras.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147808181","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
Classification of unilinear residuated lattices 线性残馀格的分类
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-04-21 DOI: 10.1007/s00012-026-00918-x
Nikolaos Galatos, Xiao Zhuang
{"title":"Classification of unilinear residuated lattices","authors":"Nikolaos Galatos,&nbsp;Xiao Zhuang","doi":"10.1007/s00012-026-00918-x","DOIUrl":"10.1007/s00012-026-00918-x","url":null,"abstract":"<div><p>We provide a classification for the class of unilinear residuated lattices (URLs) into four natural subclasses. We give axiomatizations for each class and for the varieties they generate. We further produce constructions that show that algebras of each class can be obtained from <span>(top )</span>-unital URLs (one of the four classes); this reduces the study of all URLs to the <span>(top )</span>-unital ones, already studied in previous work. Finally we show how class operators interact with the constructions and provide descriptions of the subvariety lattices.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737974","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 uniform word problem for lattices 关于格的一致字问题
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-04-03 DOI: 10.1007/s00012-026-00930-1
C. J. Van Alten
{"title":"On the uniform word problem for lattices","authors":"C. J. Van Alten","doi":"10.1007/s00012-026-00930-1","DOIUrl":"10.1007/s00012-026-00930-1","url":null,"abstract":"<div><p>An algorithm that decides the uniform word problem for lattices is given and shown to have <span>(O(n^3))</span> running-time, which also gives an <span>(O(n^3))</span> algorithm for the quasi-equational theory of lattices. This result continues a long sequence of algorithms for this problem, starting with Skolem in 1920. The algorithm makes use of Cosmadakis’ algorithm for the uniform word problem and Freese’s algorithm for the word problem for free lattices.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00930-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606729","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
On commutative weak Heyting algebras and some of its subreducts 交换弱Heyting代数及其子约
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-03-25 DOI: 10.1007/s00012-026-00925-y
Sergio A. Celani, Hernán J. San Martín
{"title":"On commutative weak Heyting algebras and some of its subreducts","authors":"Sergio A. Celani,&nbsp;Hernán J. San Martín","doi":"10.1007/s00012-026-00925-y","DOIUrl":"10.1007/s00012-026-00925-y","url":null,"abstract":"<div><p>The variety of weak Heyting algebras corresponds to the strict implication fragment of the normal modal logic <span>(textrm{K})</span>, which is also known as the subintuitionistic local consequence of the class of all Kripke models.</p><p>In this paper we study the variety of commutative weak Heyting algebras, which is defined as the subvariety of weak Heyting algebras whose members satisfy the identity <span>(arightarrow (brightarrow c) = brightarrow (arightarrow c))</span>. We give a description of the implicative-infimum subreducts of the commutative weak Heyting algebras. Moreover, we present an equivalence for the algebraic category of commutative weak Heyting algebras, which is based in a Priestley-style duality.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560948","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
Clonoids of Boolean functions with a linear source clone and a semilattice or 0- or 1-separating target clone 具有线性源克隆和半格或0或1分离目标克隆的布尔函数的克隆体
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-03-24 DOI: 10.1007/s00012-026-00926-x
Erkko Lehtonen
{"title":"Clonoids of Boolean functions with a linear source clone and a semilattice or 0- or 1-separating target clone","authors":"Erkko Lehtonen","doi":"10.1007/s00012-026-00926-x","DOIUrl":"10.1007/s00012-026-00926-x","url":null,"abstract":"<div><p>Extending Sparks’s theorem, we determine the cardinality of the lattice of <span>((C_1,C_2))</span>-clonoids of Boolean functions for certain pairs <span>((C_1,C_2))</span> of clones of Boolean functions. Namely, when <span>(C_1)</span> is a subclone (a proper subclone, resp.) of the clone of all linear (affine) functions and <span>(C_2)</span> is a subclone of the clone generated by a semilattice operation and constants (a subclone of the clone of all 0- or 1-separating functions, resp.), then the lattice of <span>((C_1,C_2))</span>-clonoids is uncountable. Combining this fact with several earlier results, we obtain a complete classification of the cardinalities of the lattices of <span>((C_1,C_2))</span>-clonoids for all pairs <span>((C_1,C_2))</span> of clones on <span>({0,1})</span>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560833","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
Monk algebras and representability 蒙克代数与可表征性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-03-19 DOI: 10.1007/s00012-026-00927-w
Jeremy F. Alm
{"title":"Monk algebras and representability","authors":"Jeremy F. Alm","doi":"10.1007/s00012-026-00927-w","DOIUrl":"10.1007/s00012-026-00927-w","url":null,"abstract":"<div><p>In “Monk Algebras and Ramsey Theory,” <i>J. Log. Algebr. Methods Program.</i> (2022), Kramer and Maddux prove various representability results in furtherance of the goal of finding the smallest weakly representable but not representable relation algebra. They also pose many open problems. In the present paper, we address problems and issues raised by Kramer and Maddux. In particular, we prove that the algebra obtained by splitting the atoms of an <i>n</i> atom Monk algebra is representable for <span>(n=32)</span> and <span>(n=116)</span>, and hence Proposition 7 in Kramer-Maddux does not generalize. We answer Problem 1(3) in the negative: relation algebra <span>(1311_{1316})</span> is not representable. Thus <span>(1311_{1316})</span> is a good candidate for the smallest weakly representable but not representable relation algebra.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00927-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560455","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
Characterizing finitely based abelian Mal’cev varieties 表征有限基阿贝尔马尔切夫变种
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-03-19 DOI: 10.1007/s00012-026-00928-9
Mateo Muro
{"title":"Characterizing finitely based abelian Mal’cev varieties","authors":"Mateo Muro","doi":"10.1007/s00012-026-00928-9","DOIUrl":"10.1007/s00012-026-00928-9","url":null,"abstract":"<div><p>In this paper, we prove the following characterization: an abelian Mal’cev variety is finitely based if and only it has finite type, its ring of idempotent binary terms is finitely presented, and its module of unary terms is finitely presented.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00928-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560454","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: Direct finiteness of representable regular (*)-rings 修正：可表示正则(*) -环的直接有限性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-03-18 DOI: 10.1007/s00012-026-00923-0
Christian Herrmann
{"title":"Correction: Direct finiteness of representable regular (*)-rings","authors":"Christian Herrmann","doi":"10.1007/s00012-026-00923-0","DOIUrl":"10.1007/s00012-026-00923-0","url":null,"abstract":"","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559801","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 priestley DN-spaces and N-spaces 关于priestley n -空间和n -空间
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-03-17 DOI: 10.1007/s00012-026-00920-3
Changchun Xia
{"title":"On priestley DN-spaces and N-spaces","authors":"Changchun Xia","doi":"10.1007/s00012-026-00920-3","DOIUrl":"10.1007/s00012-026-00920-3","url":null,"abstract":"<div><p>Inspired by the well-known Stone’s duality and Priestley’s duality for the class of distributive lattices, Celani and Calomino built a Stone-style duality for the class of distributive nearlattices with greatest element and González presented a Priestley-style duality for the variety of DN-algebras. As we know, the category of distributive nearlattices with greatest element and the category of DN-algebras with greatest element are equivalent, then it is natural to develop the Priestley-style duality for the class of distributive nearlattices with greatest element and consider the relationship between the categories of Stone-like spaces and Priestley-like spaces both for distributive nearlattices with greatest element. In this paper, we shall modify the Stone-style duality for the class of distributive nearlattices with greatest element and present a Priestley-style duality for the class of distributive nearlattices with greatest element. Furthermore, it will be shown that the category of Priestley-like spaces with certain binary relations and the category of Stone-like spaces with certain binary relations are isomorphic.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559704","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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