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Algebra Universalis最新文献

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Normal forms and representable functions in Moisil logic Moisil逻辑中的范式和可表示函数
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-03-09 DOI: 10.1007/s00012-026-00924-z
Andrei Sipoş
{"title":"Normal forms and representable functions in Moisil logic","authors":"Andrei Sipoş","doi":"10.1007/s00012-026-00924-z","DOIUrl":"10.1007/s00012-026-00924-z","url":null,"abstract":"<div><p>In this note, we determine, by a disjunctive normal form theorem, which functions on the standard <i>n</i>-nuanced Łukasiewicz-Moisil algebra are representable by formulas and we show how this result may help in establishing the structure of the free algebras in this class.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00924-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440872","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
Totally ordered inverse commutative residuated lattices 全序逆交换剩馀格
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-03-06 DOI: 10.1007/s00012-026-00922-1
Wei Chen, Shangyang Wu
{"title":"Totally ordered inverse commutative residuated lattices","authors":"Wei Chen,&nbsp;Shangyang Wu","doi":"10.1007/s00012-026-00922-1","DOIUrl":"10.1007/s00012-026-00922-1","url":null,"abstract":"<div><p>In this paper, we introduce inverse commutative residuated lattices and study some special ones, namely, totally ordered inverse commutative residuated lattices. After obtaining some properties of such inverse commutative residuated lattices, we establish a structure theorem for totally ordered inverse commutative residuated lattices. As an application, we make use of the structure theorem to prove that the variety generated by all totally ordered inverse commutative residuated lattices is arithmetical, congruence extensible and <i>e</i>-regular.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362795","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
(mu )-elements: An extension of essential elements (mu )-elements：基本元素的延伸
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-03-06 DOI: 10.1007/s00012-026-00919-w
Elena Caviglia, Amartya Goswami, Luca Mesiti
{"title":"(mu )-elements: An extension of essential elements","authors":"Elena Caviglia,&nbsp;Amartya Goswami,&nbsp;Luca Mesiti","doi":"10.1007/s00012-026-00919-w","DOIUrl":"10.1007/s00012-026-00919-w","url":null,"abstract":"<div><p>We introduce and study <span>(mu )</span>-elements of integral commutative quantales, that generalize a lattice-theoretic abstraction (namely, essential elements) of essential ideals of rings, essential submodules of modules, and dense subsets of topological spaces. Exploring several examples, we show that <span>(mu )</span>-elements are indeed a genuine extension of essential elements. We study preservation of <span>(mu )</span>-elements under contractions and extensions of quantale homomorphisms. We introduce <span>(mu )</span>-complements and <span>(mu )</span>-closedness and study their properties. We determine <span>(mu )</span>-elements for several distinguished quantales, including ideals of <span>(mathbb {Z}_n)</span> and open subsets of topological spaces. Finally, we provide a complete characterization of <span>(mu )</span>-elements in modular quantales.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00919-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147362794","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
Hoops equipped with square roots 带有平方根的圆环
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-02-25 DOI: 10.1007/s00012-026-00917-y
Anatolij Dvurečenskij, Omid Zahiri
{"title":"Hoops equipped with square roots","authors":"Anatolij Dvurečenskij,&nbsp;Omid Zahiri","doi":"10.1007/s00012-026-00917-y","DOIUrl":"10.1007/s00012-026-00917-y","url":null,"abstract":"<div><p>This paper investigates the existence and structure of square roots in hoops, with a particular focus on cancellative, Wajsberg, and basic hoops that are not necessarily bounded. We introduce novel characterizations and decomposition theorems in this context. Specifically, we show that a cancellative hoop <span>(textbf{N}(G))</span>, arising from the negative cone of an Abelian <span>(ell )</span>-group <span>(textbf{G})</span>, admits a square root <span>(mu )</span> if and only if <span>(textbf{G})</span> is two-divisible. For Wajsberg hoops with square roots, we introduce the notion of strong strict square roots and prove that any such hoop admits a unique decomposition into a direct product of a strong strict hoop and an idempotent hoop (which is, equivalently, a generalized Boolean algebra), by employing the framework of a nested family of hoops. We also investigate square roots on ordinal sums of hoops and define the ordinal sum of a family of square roots. This approach enables us to characterize linearly ordered hoops admitting square roots. Finally, we extend these results to basic hoops with square roots and identify generators for certain special subvarieties within this class.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00917-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342031","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
What is the weakest idempotent Maltsev condition that implies that abelian tolerances generate abelian congruences? 暗示阿贝尔容限产生阿贝尔同余的最弱幂等Maltsev条件是什么？
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-02-19 DOI: 10.1007/s00012-026-00915-0
Keith A. Kearnes, Emil W. Kiss
{"title":"What is the weakest idempotent Maltsev condition that implies that abelian tolerances generate abelian congruences?","authors":"Keith A. Kearnes,&nbsp;Emil W. Kiss","doi":"10.1007/s00012-026-00915-0","DOIUrl":"10.1007/s00012-026-00915-0","url":null,"abstract":"<div><p>We answer the question in the title. In the process, we correct an error in our AMS Memoir <i>The Shape of Congruence Lattices</i>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-026-00915-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340783","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 to Identical inclusions of semilattices 修正相同的包含半格
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2026-01-23 DOI: 10.1007/s00012-025-00914-7
G. Mashevitzky
{"title":"Correction to Identical inclusions of semilattices","authors":"G. Mashevitzky","doi":"10.1007/s00012-025-00914-7","DOIUrl":"10.1007/s00012-025-00914-7","url":null,"abstract":"","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146027228","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 monotone or discriminator source clone 具有单调或鉴别器源克隆的布尔函数的克隆
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-12-22 DOI: 10.1007/s00012-025-00909-4
Erkko Lehtonen
{"title":"Clonoids of Boolean functions with a monotone or discriminator source clone","authors":"Erkko Lehtonen","doi":"10.1007/s00012-025-00909-4","DOIUrl":"10.1007/s00012-025-00909-4","url":null,"abstract":"<div><p>Extending Sparks’s theorem, we determine the cardinality of the lattice of <span>((C_1,C_2))</span>-clonoid of Boolean functions in the cases where the target clone <span>(C_2)</span> is the clone of projections. Moreover, we explicitly describe the <span>((C_1,C_2))</span>-clonoid of Boolean functions in the cases where the source clone <span>(C_1)</span> is one of the four clones of monotone functions or contains the discriminator function.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145831419","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
Enriched Płonka sums 浓缩Płonka总和
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-12-12 DOI: 10.1007/s00012-025-00910-x
Ludovico Fusco, Francesco Paoli
{"title":"Enriched Płonka sums","authors":"Ludovico Fusco,&nbsp;Francesco Paoli","doi":"10.1007/s00012-025-00910-x","DOIUrl":"10.1007/s00012-025-00910-x","url":null,"abstract":"<div><p>Płonka sums are a powerful technique for the representation of algebras in regular varieties. However, certain representations of algebras in irregular varieties—like Polin’s variety or the variety of pseudocomplemented semilattices—bear striking similarities to Płonka sums, although they differ from them in some important respects. We aim at finding a convenient umbrella under which these constructions, as well as other ones of a similar kind, can be subsumed. Inspired by Grätzer and Sichler’s work on <i>Agassiz sums</i>, we appropriately enrich the structure of semilattice direct systems and we modify the attendant definition of a sum, while still encompassing Płonka sums as a special case. We prove that the above-mentioned representations of Polin algebras and pseudocomplemented semilattices can be recast in terms of this new framework. Finally, we investigate the problem as to which identities are preserved by the construction.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00910-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145730179","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 retract varieties of algebras 关于代数的可伸缩变种
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-12-05 DOI: 10.1007/s00012-025-00913-8
Emília Halušková, Danica Jakubíková-Studenovská
{"title":"On retract varieties of algebras","authors":"Emília Halušková,&nbsp;Danica Jakubíková-Studenovská","doi":"10.1007/s00012-025-00913-8","DOIUrl":"10.1007/s00012-025-00913-8","url":null,"abstract":"<div><p>A retract variety is defined as a class of algebras closed under isomorphisms, retracts and products. Let a principal retract variety be generated by one algebra and a set-principal retract variety be generated by some set of algebras. It is shown that (a) not each set-principal retract variety is principal, and (b) not each retract variety is set-principal. A class of connected monounary algebras <span>({mathcal {S}})</span> such that every retract variety of monounary algebras is generated by algebras that have all connected components from <span>({mathcal {S}})</span> and at most two connected components are isomorphic is defined, this generating class is constructively described. All set-principal retract varieties of monounary algebras are characterized via degree function of monounary algebras.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145675302","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
Functional monadic ortholattices and locally finite (sigma )-free polyadic ortholattices 泛函一元正正交与局部有限(sigma )自由多元正正交
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-12-05 DOI: 10.1007/s00012-025-00912-9
Chun-Yu Lin, Joseph McDonald
{"title":"Functional monadic ortholattices and locally finite (sigma )-free polyadic ortholattices","authors":"Chun-Yu Lin,&nbsp;Joseph McDonald","doi":"10.1007/s00012-025-00912-9","DOIUrl":"10.1007/s00012-025-00912-9","url":null,"abstract":"<div><p>In this paper, we show that every monadic ortholattice is isomorphic to a functional one, thereby resolving a recent question posed by Harding. We then study certain substitution-free reducts of the polyadic ortholattices, which we call <i>locally finite</i> <span>(sigma )</span>-<i>free polyadic ortholattices</i>, and demonstrate that they stand in a one-to-one correspondence with the locally finite diagonal-free cylindric ortholattices.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"87 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145675301","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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