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Algebra Universalis最新文献

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On the variety generated by generalized subreducts of Tarski’s algebras of relations 关于Tarski关系代数的广义子导生成的多样性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-09-01 DOI: 10.1007/s00012-023-00826-4
Dmitry A. Bredikhin
{"title":"On the variety generated by generalized subreducts of Tarski’s algebras of relations","authors":"Dmitry A. Bredikhin","doi":"10.1007/s00012-023-00826-4","DOIUrl":"10.1007/s00012-023-00826-4","url":null,"abstract":"<div><p>In the paper, a basis of identities for the variety generated by the class of groupoids that are generalized subreducts of Tarski’s algebra of relations is found. It is also proved that the corresponding class of groupoids does not form a variety.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43265355","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
Automorphisms and strongly invariant relations 自同构与强不变关系
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-08-09 DOI: 10.1007/s00012-023-00818-4
Ferdinand Börner, Martin Goldstern, Saharon Shelah
{"title":"Automorphisms and strongly invariant relations","authors":"Ferdinand Börner,&nbsp;Martin Goldstern,&nbsp;Saharon Shelah","doi":"10.1007/s00012-023-00818-4","DOIUrl":"10.1007/s00012-023-00818-4","url":null,"abstract":"<div><p>We investigate characterizations of the Galois connection <span>({{,textrm{Aut},}})</span>-<span>({{,textrm{sInv},}})</span> between sets of finitary relations on a base set <i>A</i> and their automorphisms. In particular, for <span>(A=omega _1)</span>, we construct a countable set <i>R</i> of relations that is closed under all invariant operations on relations and under arbitrary intersections, but is not closed under <span>({textrm{sInv Aut}})</span>. Our structure (<i>A</i>, <i>R</i>) has an <span>(omega )</span>-categorical first order theory. A higher order definable well-order makes it rigid, but any reduct to a finite language is homogeneous.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00818-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50464834","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
Jónsson Jónsson–Tarski algebras Jónsson-Jónsson Tarski代数
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-07-26 DOI: 10.1007/s00012-023-00824-6
Jordan DuBeau
{"title":"Jónsson Jónsson–Tarski algebras","authors":"Jordan DuBeau","doi":"10.1007/s00012-023-00824-6","DOIUrl":"10.1007/s00012-023-00824-6","url":null,"abstract":"<div><p>By studying the variety of Jónsson–Tarski algebras, we demonstrate two obstacles to the existence of large Jónsson algebras in certain varieties. First, if an algebra <i>J</i> in a language <i>L</i> has cardinality greater than <span>(|L|^+)</span> and a distributive subalgebra lattice, then it must have a proper subalgebra of size |<i>J</i>|. Second, if an algebra <i>J</i> in a language <i>L</i> satisfies <span>({{,textrm{cf},}}(|J|) &gt; 2^{|L|^+})</span> and lies in a residually small variety, then it again must have a proper subalgebra of size |<i>J</i>|. We apply the first result to show that Jónsson algebras in the variety of Jónsson–Tarski algebras cannot have cardinality greater than <span>(aleph _1)</span>. We also construct <span>(2^{aleph _1})</span> many pairwise nonisomorphic Jónsson algebras in this variety, thus proving that for some varieties the maximum possible number of Jónsson algebras can be achieved.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00824-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50515696","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
The modal logic of abelian groups 阿贝尔群的模态逻辑
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-07-26 DOI: 10.1007/s00012-023-00821-9
Sören Berger, Alexander Christensen Block, Benedikt Löwe
{"title":"The modal logic of abelian groups","authors":"Sören Berger,&nbsp;Alexander Christensen Block,&nbsp;Benedikt Löwe","doi":"10.1007/s00012-023-00821-9","DOIUrl":"10.1007/s00012-023-00821-9","url":null,"abstract":"<div><p>We prove that the modal logic of abelian groups with the accessibility relation of being isomorphic to a subgroup is <span>(mathsf {S4.2})</span>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00821-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47568534","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
Existential relations on infinite structures 无限结构上的存在关系
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-07-19 DOI: 10.1007/s00012-023-00819-3
Boris A. Romov
{"title":"Existential relations on infinite structures","authors":"Boris A. Romov","doi":"10.1007/s00012-023-00819-3","DOIUrl":"10.1007/s00012-023-00819-3","url":null,"abstract":"<div><p>We establish a criterion for a structure <i>M</i> on an infinite domain to have the Galois closure <span>({{,textrm{InvAut},}}(M))</span> (the set all relations on the domain of <i>M</i> that are invariant to all automorphisms of <i>M</i>) defined via infinite Boolean combinations of infinite (constructed by infinite conjunction) existential relations from <i>M</i>. Based on this approach, we present criteria for quantifier elimination in <i>M</i> via finite partial automorphisms of all existential relations from <i>M</i>, as well as criteria for (weak) homogeneity of <i>M</i>. Then we describe properties of <i>M</i> with a countable signature, for which the set of all relations, expressed by quantifier-fee formulas over <i>M</i>, is weakly inductive, that is, this set is closed under any infinitary intersection of the same arity relations. It is shown that the last condition is equivalent: for every <span>(n ge 1)</span> there are only finitely many isomorphism types for substructures of <i>M</i> generated by <i>n</i> elements. In case of algebras with a countable signature such type can be defined by the set of all solutions of a finite system of equations and inequalities produced by <i>n</i>-ary terms over those algebras. Next, we prove that for a finite <i>M</i> with a finite signature the problem of the description of any relation from <span>({{,textrm{InvAut},}}(M))</span> via the first order formula over <i>M</i>, which expresses it, is algorithmically solvable.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46019463","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
Topological representations of Lawson compact algebraic L-domains and Scott domains Lawson紧代数l -域和Scott域的拓扑表示
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-07-17 DOI: 10.1007/s00012-023-00820-w
Longchun Wang, Xiangnan Zhou, Qingguo Li
{"title":"Topological representations of Lawson compact algebraic L-domains and Scott domains","authors":"Longchun Wang, Xiangnan Zhou, Qingguo Li","doi":"10.1007/s00012-023-00820-w","DOIUrl":"https://doi.org/10.1007/s00012-023-00820-w","url":null,"abstract":"","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51690377","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
Topological representations of Lawson compact algebraic L-domains and Scott domains Lawson紧代数L-域和Scott域的拓扑表示
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-07-17 DOI: 10.1007/s00012-023-00820-w
Longchun Wang, Xiangnan Zhou, Qingguo Li
{"title":"Topological representations of Lawson compact algebraic L-domains and Scott domains","authors":"Longchun Wang,&nbsp;Xiangnan Zhou,&nbsp;Qingguo Li","doi":"10.1007/s00012-023-00820-w","DOIUrl":"10.1007/s00012-023-00820-w","url":null,"abstract":"<div><p>In this paper, the relationships between two important subclasses of algebraic dcpos and topological spaces which may not be <span>(textrm{T}_0)</span> are discussed. The concepts of CFF-spaces and strong CFF-spaces are introduced by considering the properties of their topological bases. With these concepts, Lawson compact algebraic L-domains and Scott domains are successfully represented in purely topological terms. Moreover, equivalences of the categories corresponding to these two subclasses of algebraic dcpos are also provided. This opens a way of finding non-<span>(textrm{T}_0)</span> topological characterizations for domains.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00820-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50489900","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
Two results on Fremlin’s Archimedean Riesz space tensor product 关于Fremlin的阿基米德-里兹空间张量积的两个结果
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-07-14 DOI: 10.1007/s00012-023-00822-8
Gerard Buskes, Page Thorn
{"title":"Two results on Fremlin’s Archimedean Riesz space tensor product","authors":"Gerard Buskes,&nbsp;Page Thorn","doi":"10.1007/s00012-023-00822-8","DOIUrl":"10.1007/s00012-023-00822-8","url":null,"abstract":"<div><p>In this paper, we characterize when, for any infinite cardinal <span>(alpha )</span>, the Fremlin tensor product of two Archimedean Riesz spaces (see Fremlin in Am J Math 94:777–798, 1972) is Dedekind <span>(alpha )</span>-complete. We also provide an example of an ideal <i>I</i> in an Archimedean Riesz space <i>E</i> such that the Fremlin tensor product of <i>I</i> with itself is not an ideal in the Fremlin tensor product of <i>E</i> with itself.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49349135","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: 4
Weakly Schreier extensions for general algebras 一般代数的弱Schreier扩张
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-07-14 DOI: 10.1007/s00012-023-00823-7
Graham Manuell, Nelson Martins-Ferreira
{"title":"Weakly Schreier extensions for general algebras","authors":"Graham Manuell,&nbsp;Nelson Martins-Ferreira","doi":"10.1007/s00012-023-00823-7","DOIUrl":"10.1007/s00012-023-00823-7","url":null,"abstract":"<div><p>Weakly Schreier split extensions are a reasonably large, yet well-understood class of monoid extensions, which generalise some aspects of split extensions of groups. This short note provides a way to define and study similar classes of split extensions in general algebraic structures (parameterised by a term <span>(theta )</span>). These generalise weakly Schreier extensions of monoids, as well as general extensions of semi-abelian varieties (using the <span>(theta )</span> appearing in their syntactic characterisation). Restricting again to the case of monoids, a different choice of <span>(theta )</span> leads to a new class of monoid extensions, more general than the weakly Schreier split extensions.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00823-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48706451","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
Strongly minimal Steiner systems II: coordinatization and quasigroups 强极小Steiner系统II:配位与拟群
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-05-02 DOI: 10.1007/s00012-023-00812-w
John T. Baldwin
{"title":"Strongly minimal Steiner systems II: coordinatization and quasigroups","authors":"John T. Baldwin","doi":"10.1007/s00012-023-00812-w","DOIUrl":"10.1007/s00012-023-00812-w","url":null,"abstract":"<div><p>Each strongly minimal Steiner <i>k</i>-system (<i>M</i>, <i>R</i>) (where is <i>R</i> is a ternary collinearity relation) can be ‘coordinatized’ in the sense of (Ganter–Werner 1975) by a quasigroup if <i>k</i> is a prime-power. We show this coordinatization is never definable in (<i>M</i>, <i>R</i>) and the strongly minimal Steiner <i>k</i>-systems constructed in (Baldwin–Paolini 2020) never interpret a quasigroup. Nevertheless, by refining the construction, if <i>k</i> is a prime power, in each (2, <i>k</i>)-variety of quasigroups (Definition 3.10) there is a strongly minimal quasigroup that interprets a Steiner <i>k</i>-system.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46913443","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: 1
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