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Algebra Universalis最新文献

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Finitely based congruence varieties 有限同余变种
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-01-12 DOI: 10.1007/s00012-023-00840-6
Ralph Freese, Paolo Lipparini
{"title":"Finitely based congruence varieties","authors":"Ralph Freese,&nbsp;Paolo Lipparini","doi":"10.1007/s00012-023-00840-6","DOIUrl":"10.1007/s00012-023-00840-6","url":null,"abstract":"<div><p>We show that for a large class of varieties of algebras, the equational theory of the congruence lattices of the members is not finitely based.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139458712","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
Semilinear De Morgan monoids and epimorphisms 半线性德摩根单体和外延
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-01-09 DOI: 10.1007/s00012-023-00837-1
J. J. Wannenburg, J. G. Raftery
{"title":"Semilinear De Morgan monoids and epimorphisms","authors":"J. J. Wannenburg,&nbsp;J. G. Raftery","doi":"10.1007/s00012-023-00837-1","DOIUrl":"10.1007/s00012-023-00837-1","url":null,"abstract":"<div><p>A representation theorem is proved for De Morgan monoids that are (i) <i>semilinear</i>, i.e., subdirect products of totally ordered algebras, and (ii) <i>negatively generated</i>, i.e., generated by lower bounds of the neutral element. Using this theorem, we prove that the De Morgan monoids satisfying (i) and (ii) form a variety—in fact, a locally finite variety. We then prove that epimorphisms are surjective in every variety of negatively generated semilinear De Morgan monoids. In the process, epimorphism-surjectivity is established for several other classes as well, including the variety of all semilinear idempotent commutative residuated lattices and all varieties of negatively generated semilinear Dunn monoids. The results settle natural questions about Beth-style definability for a range of substructural logics.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00837-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139414180","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
Priestley-style duality for DN-algebras DN 矩阵的普里斯特利式对偶性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-01-03 DOI: 10.1007/s00012-023-00838-0
Luciano J. González
{"title":"Priestley-style duality for DN-algebras","authors":"Luciano J. González","doi":"10.1007/s00012-023-00838-0","DOIUrl":"10.1007/s00012-023-00838-0","url":null,"abstract":"<div><p>The aim of this article is to develop a Priestley-style duality for the variety of DN-algebras. In order to achieve this, we use the concept of free distributive lattice extension of a DN-algebra. We establish a connection with the Priestley duality for distributive lattices. Finally, we present topological descriptions for the lattice of filters, for the lattice of congruences, and for certain kinds of subalgebras of a DN-algebra.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139102009","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
The “zero-two” law in Orlicz–Kantorovich spaces 奥尔利奇-康托洛维奇空间的 "零点二 "定律
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2024-01-03 DOI: 10.1007/s00012-023-00839-z
Inomjon Ganiev, Farrukh Mukhamedov
{"title":"The “zero-two” law in Orlicz–Kantorovich spaces","authors":"Inomjon Ganiev,&nbsp;Farrukh Mukhamedov","doi":"10.1007/s00012-023-00839-z","DOIUrl":"10.1007/s00012-023-00839-z","url":null,"abstract":"<div><p>The present paper deals with <span>(L_0)</span>-valued measures and the associated Orlicz–Kantorovich lattice. The considered Orlicz–Kantorovich lattice, endowed with the Luxemburg norm, is represented as a measurable bundle of classical Orlicz spaces associated with scalar measures. This kind of representation allows us to investigate positive contractions and apply the corresponding zero-two laws on the classical Orlicz spaces, to prove vector versions of “zero-two” laws on the considered Orlicz–Kantorovich space.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093836","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
Measuring cyber wisdom: preliminary validation of a new four-component measure. 衡量网络智慧：新的四要素衡量标准的初步验证。
IF 5.5 4区 数学
Algebra Universalis Pub Date : 2024-01-01 Epub Date: 2023-07-04 DOI: 10.1007/s10639-023-11953-9
Tom Harrison, Gianfranco Polizzi, Shane McLoughlin, Francisco Moller
{"title":"Measuring cyber wisdom: preliminary validation of a new four-component measure.","authors":"Tom Harrison, Gianfranco Polizzi, Shane McLoughlin, Francisco Moller","doi":"10.1007/s10639-023-11953-9","DOIUrl":"10.1007/s10639-023-11953-9","url":null,"abstract":"<p><p>Cyber-wisdom is the ability to know and do the right thing at the right time, when using digital technologies, and is a concept that is gaining attention from educators. Whilst the theory and practice of cyber-wisdom education is established, to date there has been no attempt to investigate how the virtue of cyber-wisdom might be measured. This is a lacuna as it limits future research in the area, including, in particular, proximal evaluations of cyber-wisdom interventions. This article introduces a new four-component measure of cyber-wisdom, which is relevant to how the virtue may be cultivated in practice via formal education and the teaching of what is generally referred to as digital citizenship education. The measure was piloted with 1,331 13-16 year-olds. The findings provide initial evidence that cyber-wisdom literacy, reasoning, reflection, and motivation can be measured. This study provides preliminary validation of cyber-wisdom sub-measures that might be used in evaluations of educational interventions that seek to help children and adolescents live with wisdom in the digital age.</p>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"11 1","pages":"4317-4336"},"PeriodicalIF":5.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10923952/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73906343","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 a statement of O. Frink about free pseudo-complemented meet-semilattices O.弗林克关于自由伪补满足半方阵的声明
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-12-14 DOI: 10.1007/s00012-023-00836-2
Tibor Katriňák, Jaroslav Guričan
{"title":"On a statement of O. Frink about free pseudo-complemented meet-semilattices","authors":"Tibor Katriňák,&nbsp;Jaroslav Guričan","doi":"10.1007/s00012-023-00836-2","DOIUrl":"10.1007/s00012-023-00836-2","url":null,"abstract":"<div><p>Orrin Frink in 1962 stated incorrectly, that there exist free pseudocomplemented meet-semilattices, which are not lattices. This is disproved in the present paper. We have shown that any free PCS is in fact a sectionally pseudocomplemented lattice.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00836-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138630650","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
Majority-closed minions of Boolean functions 布尔函数的多数闭仆从
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-11-22 DOI: 10.1007/s00012-023-00835-3
Erkko Lehtonen
{"title":"Majority-closed minions of Boolean functions","authors":"Erkko Lehtonen","doi":"10.1007/s00012-023-00835-3","DOIUrl":"10.1007/s00012-023-00835-3","url":null,"abstract":"<div><p>The 93 minions of Boolean functions stable under left composition with the clone of self-dual monotone functions are described. As an easy consequence, all <span>((C_1,C_2))</span>-clonoids of Boolean functions are determined for an arbitrary clone <span>(C_1)</span> and for any clone <span>(C_2)</span> containing the clone of self-dual monotone functions.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138431495","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: 3
Esakia duals of regular Heyting algebras 正则Heyting代数的Esakia对偶
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-11-21 DOI: 10.1007/s00012-023-00833-5
Gianluca Grilletti, Davide Emilio Quadrellaro
{"title":"Esakia duals of regular Heyting algebras","authors":"Gianluca Grilletti,&nbsp;Davide Emilio Quadrellaro","doi":"10.1007/s00012-023-00833-5","DOIUrl":"10.1007/s00012-023-00833-5","url":null,"abstract":"<div><p>We investigate in this article regular Heyting algebras by means of Esakia duality. In particular, we give a characterisation of Esakia spaces dual to regular Heyting algebras and we show that there are continuum-many varieties of Heyting algebras generated by regular Heyting algebras. We also study several logical applications of these classes of objects and we use them to provide novel topological completeness theorems for inquisitive logic, <span>(texttt{DNA})</span>-logics and dependence logic.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-023-00833-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138431642","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
Surjective polymorphisms of directed reflexive cycles 有向自反环的满射多态性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-11-17 DOI: 10.1007/s00012-023-00834-4
Isabelle Larivière, Benoît Larose, David E. Pazmiño Pullas
{"title":"Surjective polymorphisms of directed reflexive cycles","authors":"Isabelle Larivière,&nbsp;Benoît Larose,&nbsp;David E. Pazmiño Pullas","doi":"10.1007/s00012-023-00834-4","DOIUrl":"10.1007/s00012-023-00834-4","url":null,"abstract":"<div><p>A <i>reflexive cycle</i> is any reflexive digraph whose underlying undirected graph is a cycle. Call a relational structure <i>Słupecki</i> if its surjective polymorphisms are all essentially unary. We prove that all reflexive cycles of girth at least 4 have this property.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138138477","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
Choice-free topological duality for implicative lattices and Heyting algebras 隐含格和Heyting代数的无选择拓扑对偶性
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2023-11-14 DOI: 10.1007/s00012-023-00830-8
Chrysafis Hartonas
{"title":"Choice-free topological duality for implicative lattices and Heyting algebras","authors":"Chrysafis Hartonas","doi":"10.1007/s00012-023-00830-8","DOIUrl":"10.1007/s00012-023-00830-8","url":null,"abstract":"<div><p>We develop a common semantic framework for the interpretation both of <span>({textbf {IPC}})</span>, the intuitionistic propositional calculus, and of logics weaker than <span>({textbf {IPC}})</span> (substructural and subintuitionistic logics). To this end, we prove a choice-free representation and duality theorem for implicative lattices, which may or may not be distributive. The duality specializes to a choice-free duality for the full subcategory of Heyting algebras and a category of topological sorted frames with a ternary sorted relation.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878336","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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