Algebra Universalis最新文献

Correction: Projectivity in (bounded) commutative integral residuated lattices 修正：（有界）交换积分残差格中的投影

IF 0.6 4区数学

Algebra Universalis Pub Date : 2025-01-04 DOI: 10.1007/s00012-024-00879-z

Paolo Aglianò, Sara Ugolini

引用次数: 0

Algebraic frames in Priestley duality Priestley对偶中的代数框架

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-12-30 DOI: 10.1007/s00012-024-00876-2

Guram Bezhanishvili, Sebastian D. Melzer

引用次数: 0

A finite representation of relation algebra (varvec{1896_{3013}}) 关系代数的有限表示 (varvec{1896_{3013}})

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-12-30 DOI: 10.1007/s00012-024-00881-5

Jeremy F. Alm

引用次数: 0

On z-elements of multiplicative lattices 在乘法格的z元素上

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-12-28 DOI: 10.1007/s00012-024-00882-4

Amartya Goswami, Themba Dube

引用次数: 0

On complete lattices of radical submodules and ( z )-submodules 关于根子模和( z ) -子模的完全格

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-12-13 DOI: 10.1007/s00012-024-00880-6

Hosein Fazaeli Moghimi, Seyedeh Fatemeh Mohebian

{"title":"On complete lattices of radical submodules and ( z )-submodules","authors":"Hosein Fazaeli Moghimi, Seyedeh Fatemeh Mohebian","doi":"10.1007/s00012-024-00880-6","DOIUrl":"10.1007/s00012-024-00880-6","url":null,"abstract":"<div>Let M be a module over a commutative ring R, and (mathcal {R}(_{R}M)) denote the complete lattice of radical submodules of M. It is shown that if M is a multiplication R-module, then (mathcal {R}(_{R}M)) is a frame. In particular, if M is a finitely generated multiplication R-module, then (mathcal {R}(_{R}M)) is a coherent frame and if, in addition, M is faithful, then the assignment (Nmapsto (N:M)_{ z }) defines a coherent map from (mathcal {R}(_{R}M)) to the coherent frame (mathcal {Z}(_{R}R)) of ( z )-ideals of R. As a generalization of ( z )-ideals, a proper submodule N of M is called a ( z )-submodule of M if for any (xin M) and (yin N) such that every maximal submodule of M containing y also contains x, then (xin N). The set of ( z )-submodules of M, denoted (mathcal {Z}(_{R}M)), forms a complete lattice with respect to the order of inclusion. It is shown that if M is a finitely generated faithful multiplication R-module, then (mathcal {Z}(_{R}M)) is a coherent frame and the assignment (Nmapsto N_{ z }) (where (N_{ z }) is the intersection of all ( z )-submodules of M containing N) is a surjective coherent map from (mathcal {R}(_{R}M)) to (mathcal {Z}(_{R}M)). In particular, in this case, (mathcal {R}(_{R}M)) is a normal frame if and only if (mathcal {Z}(_{R}M)) is a normal frame.</div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821130","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

Near-unanimity-closed minions of Boolean functions 布尔函数的近乎一致封闭的爪牙

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-11-20 DOI: 10.1007/s00012-024-00872-6

Erkko Lehtonen

引用次数: 0

Multisorted Boolean clones determined by binary relations up to minion homomorphisms 由二元关系决定的多分类布尔克隆，直至奴仆同态

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-11-06 DOI: 10.1007/s00012-024-00878-0

Libor Barto, Maryia Kapytka

引用次数: 0

Exploring new topologies for the theory of clones 探索克隆理论的新拓扑结构

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-11-01 DOI: 10.1007/s00012-024-00877-1

Antonio Bucciarelli, Antonino Salibra

{"title":"Exploring new topologies for the theory of clones","authors":"Antonio Bucciarelli, Antonino Salibra","doi":"10.1007/s00012-024-00877-1","DOIUrl":"10.1007/s00012-024-00877-1","url":null,"abstract":"<div>Clones of operations of arity (omega ) (referred to as (omega )-operations) have been employed by Neumann to represent varieties of infinitary algebras defined by operations of at most arity (omega ). More recently, clone algebras have been introduced to study clones of functions, including (omega )-operations, within the framework of one-sorted universal algebra. Additionally, polymorphisms of arity (omega ), which are (omega )-operations preserving the relations of a given first-order structure, have recently been used to establish model theory results with applications in the field of complexity of CSP problems. In this paper, we undertake a topological and algebraic study of polymorphisms of arity (omega ) and their corresponding invariant relations. Given a Boolean ideal X on the set (A^omega ), we endow the set of (omega )-operations on A with a topology, which we refer to as X-topology. Notably, the topology of pointwise convergence can be retrieved as a special case of this approach. Polymorphisms and invariant relations are then defined parametrically with respect to the X-topology. We characterise the X-closed clones of (omega )-operations in terms of (textrm{Pol}^omega )-(textrm{Inv}^omega ) and present a method to relate (textrm{Inv}^omega )-(textrm{Pol}^omega ) to the classical (finitary) (textrm{Inv})-(textrm{Pol}).</div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142565894","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

Graphs of finite algebras: edges, and connectivity 有限代数的图：边和连通性

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-10-30 DOI: 10.1007/s00012-024-00865-5

Andrei A. Bulatov

{"title":"Graphs of finite algebras: edges, and connectivity","authors":"Andrei A. Bulatov","doi":"10.1007/s00012-024-00865-5","DOIUrl":"10.1007/s00012-024-00865-5","url":null,"abstract":"<div>We refine and advance the study of the local structure of idempotent finite algebras started in Bulatov (LICS, 2004). We introduce a graph-like structure on an arbitrary finite idempotent algebra including those admitting type 1. We show that this graph is connected, its edges can be classified into 4 types corresponding to the local behavior (set, semilattice, majority, or affine) of certain term operations. We also show that if the variety generated by the algebra omits type 1, then the structure of the algebra can be ‘improved’ without introducing type 1 by choosing an appropriate reduct of the original algebra. Taylor minimal idempotent algebras introduced recently are a special case of such reducts. Then we refine this structure demonstrating that the edges of the graph of an algebra omitting type 1 can be made ‘thin’, that is, there are term operations that behave very similar to semilattice, majority, or affine operations on 2-element subsets of the algebra. Finally, we prove certain connectivity properties of the refined structures. This research is motivated by the study of the Constraint Satisfaction Problem, although the problem itself does not really show up in this paper.</div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"85 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555291","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

Some remarks on type n lattice-ordered algebras and a question of Huijsmans 关于 n 型格序代数的一些评论和惠伊斯曼斯的一个问题

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-10-18 DOI: 10.1007/s00012-024-00875-3

Ayşe Uyar

引用次数: 0