发布求助
文献互助 智能选刊 最新文献

Algebra Universalis最新文献

筛选
英文 中文
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":"84 1","pages":""},"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":"84 3","pages":""},"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":"84 3","pages":""},"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":"84 3","pages":""},"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":"84 2","pages":""},"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
Admissible subsets and completions of ordered algebras 序代数的可容许子集与完备
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-04-28 DOI: 10.1007/s00012-023-00813-9
Valdis Laan, Jianjun Feng, Xia Zhang
{"title":"Admissible subsets and completions of ordered algebras","authors":"Valdis Laan,&nbsp;Jianjun Feng,&nbsp;Xia Zhang","doi":"10.1007/s00012-023-00813-9","DOIUrl":"10.1007/s00012-023-00813-9","url":null,"abstract":"<div><p>We consider ordered universal algebras and give a construction of a join-completion for them using so-called <span>(mathscr {D})</span>-ideals. We show that this construction has a universal property that induces a reflector from a certain category of ordered algebras to the category of sup-algebras. Our results generalize several earlier known results about different ordered structures.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"84 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46428447","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
Stone space partitions indexed by a poset 由偏序集索引的Stone空间分区
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-04-27 DOI: 10.1007/s00012-023-00816-6
Andrew B. Apps
{"title":"Stone space partitions indexed by a poset","authors":"Andrew B. Apps","doi":"10.1007/s00012-023-00816-6","DOIUrl":"10.1007/s00012-023-00816-6","url":null,"abstract":"<div><p>Stone space partitions <span>({X_{p}mid pin P})</span> satisfying conditions like <span>(overline{X_{p}}=bigcup _{qleqslant p}X_{q})</span> for all <span>(pin P)</span>, where <i>P</i> is a poset or PO system (poset with a distinguished subset), arise naturally in the study both of primitive Boolean algebras and of <span>(omega )</span>-categorical structures. A key concept for studying such partitions is that of a <i>p</i>-trim open set which meets precisely those <span>(X_{q})</span> for which <span>(qgeqslant p)</span>; for Stone spaces, this is the topological equivalent of a pseudo-indecomposable set. This paper develops the theory of infinite partitions of Stone spaces indexed by a poset or PO system where the trim sets form a neighbourhood base for the topology. We study the interplay between order properties of the poset/PO system and topological properties of the partition, examine extensions and completions of such partitions, and derive necessary and sufficient conditions on the poset/PO system for the existence of the various types of partition studied. We also identify circumstances in which a second countable Stone space with a trim partition indexed by a given PO system is unique up to homeomorphism, subject to choices on the isolated point structure and boundedness of the partition elements. One corollary of our results is that there is a partition <span>({X_{r}mid rin [0,1]})</span> of the Cantor set such that <span>(overline{X_{r}}=bigcup _{sleqslant r}X_{s}text { for all }rin [0,1])</span>.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"84 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49544457","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: 2
Topology of closure systems in algebraic lattices 代数格中闭包系统的拓扑
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-04-25 DOI: 10.1007/s00012-023-00815-7
Niels Schwartz
{"title":"Topology of closure systems in algebraic lattices","authors":"Niels Schwartz","doi":"10.1007/s00012-023-00815-7","DOIUrl":"10.1007/s00012-023-00815-7","url":null,"abstract":"<div><p>Algebraic lattices are spectral spaces for the coarse lower topology. Closure systems in algebraic lattices are studied as subspaces. Connections between order theoretic properties of a closure system and topological properties of the subspace are explored. A closure system is algebraic if and only if it is a patch closed subset of the ambient algebraic lattice. Every subset <i>X</i> in an algebraic lattice <i>P</i> generates a closure system <span>(langle X rangle _P)</span>. The closure system <span>(langle Y rangle _P)</span> generated by the patch closure <i>Y</i> of <i>X</i> is the patch closure of <span>(langle X rangle _P)</span>. If <i>X</i> is contained in the set of nontrivial prime elements of <i>P</i> then <span>(langle X rangle _P)</span> is a frame and is a coherent algebraic frame if <i>X</i> is patch closed in <i>P</i>. Conversely, if the algebraic lattice <i>P</i> is coherent then its set of nontrivial prime elements is patch closed.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"84 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00815-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41700899","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
Extremality, left-modularity and semidistributivity 极值、左模性和半分布性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-04-17 DOI: 10.1007/s00012-023-00814-8
Henri Mühle
{"title":"Extremality, left-modularity and semidistributivity","authors":"Henri Mühle","doi":"10.1007/s00012-023-00814-8","DOIUrl":"10.1007/s00012-023-00814-8","url":null,"abstract":"<div><p>In this article we study the relations between three classes of lattices each extending the class of distributive lattices in a different way. In particular, we consider join-semidistributive, join-extremal and left-modular lattices, respectively. Our main motivation is a recent result by Thomas and Williams proving that every semidistributive, extremal lattice is left modular. We prove the converse of this on a slightly more general level. Our main result asserts that every join-semidistributive, left-modular lattice is join extremal. We also relate these properties to the topological notion of lexicographic shellability.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"84 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00814-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50488428","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: 1
Extremality, left-modularity and semidistributivity 极值性、左模性和半分配性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-04-17 DOI: 10.1007/s00012-023-00814-8
Henri Mühle
{"title":"Extremality, left-modularity and semidistributivity","authors":"Henri Mühle","doi":"10.1007/s00012-023-00814-8","DOIUrl":"https://doi.org/10.1007/s00012-023-00814-8","url":null,"abstract":"","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"84 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51690512","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信