Algebra Universalis最新文献_第3页

Quasivarieties of algebras whose compact relative congruences are principal 其紧凑相对全等为主项的代数准变量

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-08-27 DOI: 10.1007/s00012-024-00866-4

Anvar M. Nurakunov

引用次数: 0

Override and restricted union for partial functions 部分函数的覆盖和受限联合

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-08-12 DOI: 10.1007/s00012-024-00864-6

Tim Stokes

{"title":"Override and restricted union for partial functions","authors":"Tim Stokes","doi":"10.1007/s00012-024-00864-6","DOIUrl":"10.1007/s00012-024-00864-6","url":null,"abstract":"<div>The override operation (sqcup ) is a natural one in computer science, and has connections with other areas of mathematics such as hyperplane arrangements. For arbitrary functions f and g, (fsqcup g) is the function with domain ({{,textrm{dom},}}(f)cup {{,textrm{dom},}}(g)) that agrees with f on ({{,textrm{dom},}}(f)) and with g on ({{,textrm{dom},}}(g) backslash {{,textrm{dom},}}(f)). Jackson and the author have shown that there is no finite axiomatisation of algebras of functions of signature ((sqcup )). But adding operations (such as update) to this minimal signature can lead to finite axiomatisations. For the functional signature ((sqcup ,backslash )) where (backslash ) is set-theoretic difference, Cirulis has given a finite equational axiomatisation as subtraction o-semilattices. Define (fcurlyvee g=(fsqcup g)cap (gsqcup f)) for all functions f and g; this is the largest domain restriction of the binary relation (fcup g) that gives a partial function. Now (fcap g=fbackslash (fbackslash g)) and (fsqcup g=fcurlyvee (fcurlyvee g)) for all functions f, g, so the signatures ((curlyvee )) and ((sqcup ,cap )) are both intermediate between ((sqcup )) and ((sqcup ,backslash )) in expressive power. We show that each is finitely axiomatised, with the former giving a proper quasivariety and the latter the variety of associative distributive o-semilattices in the sense of Cirulis.</div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00864-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202461","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

(varvec{S})-preclones and the Galois connection (varvec{{}^{S}{}textrm{Pol}})–(varvec{{}^{S}{}textrm{Inv}}), Part I $$varvec{S}$ -preclones and Galois connection $$varvec{{}^{S}{}textrm{Pol}}$ - $$varvec{{}^{S}{}textrm{Inv}}$, Part I

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-07-09 DOI: 10.1007/s00012-024-00863-7

Peter Jipsen, Erkko Lehtonen, Reinhard Pöschel

{"title":"(varvec{S})-preclones and the Galois connection (varvec{{}^{S}{}textrm{Pol}})–(varvec{{}^{S}{}textrm{Inv}}), Part I","authors":"Peter Jipsen, Erkko Lehtonen, Reinhard Pöschel","doi":"10.1007/s00012-024-00863-7","DOIUrl":"10.1007/s00012-024-00863-7","url":null,"abstract":"<div>We consider S-operations (f :A^{n} rightarrow A) in which each argument is assigned a signum (s in S) representing a “property” such as being order-preserving or order-reversing with respect to a fixed partial order on A. The set S of such properties is assumed to have a monoid structure reflecting the behaviour of these properties under the composition of S-operations (e.g., order-reversing composed with order-reversing is order-preserving). The collection of all S-operations with prescribed properties for their signed arguments is not a clone (since it is not closed under arbitrary identification of arguments), but it is a preclone with special properties, which leads to the notion of S-preclone. We introduce S-relations (varrho = (varrho _{s})_{s in S}), S-relational clones, and a preservation property (<img>), and we consider the induced Galois connection ({}^{S}{}textrm{Pol})–({}^{S}{}textrm{Inv}). The S-preclones and S-relational clones turn out to be exactly the closed sets of this Galois connection. We also establish some basic facts about the structure of the lattice of all S-preclones on A.</div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00863-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568120","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 the networks of large embeddings 关于大型嵌入网络

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-07-09 DOI: 10.1007/s00012-024-00862-8

Tuğba Aslan, Mohamed Khaled, Gergely Székely

引用次数: 0

The Freudenthal and other compactifications of continuous frames 弗赖登塔尔法和其他连续框架压缩法

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-07-04 DOI: 10.1007/s00012-024-00857-5

Simo Mthethwa, Gugulethu Nogwebela

引用次数: 0

Unilinear residuated lattices: axiomatization, varieties and FEP 单线性残差网格：公理化、品种和 FEP

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-06-21 DOI: 10.1007/s00012-024-00856-6

Nikolaos Galatos, Xiao Zhuang

引用次数: 0

A structure theorem for truncations on an Archimedean vector lattice 阿基米德向量网格截断的结构定理

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-06-21 DOI: 10.1007/s00012-024-00858-4

Karim Boulabiar

{"title":"A structure theorem for truncations on an Archimedean vector lattice","authors":"Karim Boulabiar","doi":"10.1007/s00012-024-00858-4","DOIUrl":"10.1007/s00012-024-00858-4","url":null,"abstract":"<div>Let X be an Archimedean vector lattice and (X_{+}) denote the positive cone of X. A unary operation (varpi ) on (X_{+}) is called a truncation on X if <div><div>$$begin{aligned} xwedge varpi left( yright) =varpi left( xright) wedge yquad text {for all }x,yin X_{+}. end{aligned}$$</div></div>Let (X^{u}) denote the universal completion of X with a distinguished weak element (e>0.) It is shown that a unary operation (varpi ) on (X_{+}) is a truncation on X if and only if there exists an element (uin X^{u}) and a component p of e such that <div><div>$$begin{aligned} pwedge u=0quad text {and}quad varpi left( xright) =px+uwedge x text {for all }xin X_{+}. end{aligned}$$</div></div>Here, px is the product of p and x with respect to the unique lattice-ordered multiplication in (X^{u}) having e as identity. As an example of illustration, if (varpi ) is a truncation on some (L_{p}left( {mu } right) )-space then there exists a measurable set A and a function (uin L_{0}left( {mu } right) ) vanishing on A such that (varpi left( xright) =1_{A}x+uwedge x) for all (xin L_{p}left( {mu } right) .)</div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506984","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

Characterization of self-majorizing elements in Archimedean vector lattices 阿基米德向量网格中自约化元素的特征

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-06-19 DOI: 10.1007/s00012-024-00860-w

Zied Jbeli, Mohamed Ali Toumi

引用次数: 0

Slim patch lattices as absolute retracts and maximal lattices 作为绝对缩回和最大网格的薄片网格

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-06-17 DOI: 10.1007/s00012-024-00861-9

Gábor Czédli

引用次数: 0

Permutation invariant boolean states 排列不变布尔态