Algebra Universalis最新文献_第2页

Some generalized metric properties of n-semitopological groups n-半拓扑群的一些广义度量性质

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-06-23 DOI: 10.1007/s00012-025-00897-5

Fucai Lin, Xixi Qi

引用次数: 0

u-topology and m-topology on the ring of measurable functions, generalized and revisited 可测函数环上的u-拓扑和m-拓扑，推广和重访

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-06-23 DOI: 10.1007/s00012-025-00896-6

Sudip Kumar Acharyya, Atasi Debray, Pratip Nandi

{"title":"u-topology and m-topology on the ring of measurable functions, generalized and revisited","authors":"Sudip Kumar Acharyya, Atasi Debray, Pratip Nandi","doi":"10.1007/s00012-025-00896-6","DOIUrl":"10.1007/s00012-025-00896-6","url":null,"abstract":"<div>Given an ideal I in the ring (mathcal {M}(X,mathcal {A})) of all real valued measurable functions over the measurable space ((X,mathcal {A})) and a measure (mu :mathcal {A}rightarrow [0,infty ]), we introduce the (u_mu ^I)-topology and the (m_mu ^I)-topology on (mathcal {M}(X,mathcal {A})) as generalizations of the u-topology and the m-topology on (mathcal {M}(X,mathcal {A})) respectively. For a countably generated ideal I in (mathcal {M}(X,mathcal {A})), it is proved that the (u_mu ^I)-topology and the (m_mu ^I)-topology coincide if and only if (Xsetminus bigcap Z[I]) is a (mu )-bounded subset of X. The components of 0 in both of these topologies are determined and it is proved that the condition of denseness of an ideal I in (mathcal {M}(X,mathcal {A})) is equivalent in these two topologies and this happens when and only when there exists (Zin Z[I]) such that (mu (Z)=0). It is also proved that I is closed in (mathcal {M}(X,mathcal {A})) in the (m_mu )-topology if and only if it is a (Z_mu )-ideal. Two more topologies on (mathcal {M}(X,mathcal {A})) viz. the (u_{mu ,F}^I)-topology and the (m_{mu ,F}^I)-topology, finer than the (u_mu ^I)-topology and the (m_mu ^I)-topology respectively are introduced and a few relevant properties are investigated thereon.</div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144558","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

Infinitary primitive positive definability over the real numbers with convex relations 具有凸关系的实数上的无穷本原正可定义性

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-06-23 DOI: 10.1007/s00012-025-00893-9

Sebastian Meyer

引用次数: 0

Perspectivity in complemented modular lattices and regular rings 补模格与正则环的透视性

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-06-19 DOI: 10.1007/s00012-025-00894-8

Christian Herrmann

引用次数: 0

On the completeness of localic groups via generators and relations 基于生成器和关系的局部群的完备性

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-06-19 DOI: 10.1007/s00012-025-00898-4

Simo S. Mthethwa, Onesipho Ntombela

引用次数: 0

Congruence systems in dual discriminator varieties 对偶鉴别变体中的同余系统

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-05-27 DOI: 10.1007/s00012-025-00891-x

Miguel Campercholi, Diego Castaño, Gonzalo Zigarán

{"title":"Congruence systems in dual discriminator varieties","authors":"Miguel Campercholi, Diego Castaño, Gonzalo Zigarán","doi":"10.1007/s00012-025-00891-x","DOIUrl":"10.1007/s00012-025-00891-x","url":null,"abstract":"<div>A congruence system on an algebra (textbf{A}) is a tuple (langle theta _1,ldots ,theta _k,) (a_1,ldots ,a_krangle ) where (theta _1,ldots ,theta _k in mathop {textrm{Con}}textbf{A}), (a_1,ldots ,a_k in A) and (langle a_i,a_jrangle in theta _i vee theta _j) for all (i,j in {1,ldots ,k}). A solution to such a congruence system is an element (a in A) satisfying (langle a,a_irangle in theta _i) for all (i in {1,ldots ,k}). A tuple of congruences (langle theta _1,ldots , theta _krangle ) is said to be a Chinese Remainder tuple (CR tuple for short) of (textbf{A}) provided that every system (langle theta _1,ldots ,theta _k,a_1,ldots ,a_krangle ) with (a_1,ldots ,a_k in A) has a solution. Since two congruences (theta _1,theta _2) form a CR tuple if and only if they permute, the property of being a CR tuple is a generalization of the notion of permutability that makes sense for more than two congruences. The main result of this article is a characterization of CR tuples for finite algebras in dual discriminator varieties. As an application, we obtain a neat characterization of CR tuples for finite distributive lattices.</div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145145547","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

Profinite bi-Heyting algebras 无限双heyting代数

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-05-09 DOI: 10.1007/s00012-025-00892-w

Lydia Tasiou

引用次数: 0

Compact ICA-topobooleans and the Smirnov compactification theorem 紧凑型 ICA 拓扑布尔和斯米尔诺夫紧凑化定理

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-04-07 DOI: 10.1007/s00012-025-00885-9

Ali Akbar Estaji, Rahimeh Pourkhandani, Mehdi Vatandoost

引用次数: 0

Nonelementary inclusive varieties of groups and semigroups 群和半群的非初等包容变种

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-04-04 DOI: 10.1007/s00012-025-00887-7

G. Mashevitzky

{"title":"Nonelementary inclusive varieties of groups and semigroups","authors":"G. Mashevitzky","doi":"10.1007/s00012-025-00887-7","DOIUrl":"10.1007/s00012-025-00887-7","url":null,"abstract":"<div>The class of identical inclusions was defined by E. S. Lyapin. This is the class of universal formulas which is situated strictly between identities and universal positive formulas. Classes of semigroups defined by identical inclusions are called inclusive varieties. Inclusive varieties that cannot be defined by the first order formulas are called nonelementary inclusive varieties. We study nonelementary inclusive varieties of groups, Clifford semigroups and nilsemigroups. In particular, a criterion for an inclusive variety to be nonelementary is found and limit nonelementary inclusive varieties of abelian groups are described. We also describe the upper semilattice of nonelementary inclusive varieties of finite abelian groups and prove that it is uncountable. We find an uncountable set of nonelementary inclusive varieties of nilpotent class 3 and nil class 2 finite commutative semigroups and a limit nonelementary inclusive variety of nilsemigroups. We consider completely regular semigroups in semigroup signature with an additional unary operation and nilsemigroups in semigroup signature with the additional constant 0.</div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00887-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143778067","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 structure of modal and tense operators on a boolean algebra 布尔代数上模态算子和时态算子的结构

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-04-04 DOI: 10.1007/s00012-025-00890-y

Guram Bezhanishvili, Andre Kornell

引用次数: 0