Algebra Universalis最新文献

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":null,"pages":null},"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":null,"pages":null},"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

Graphs of finite algebras: maximality, rectangularity, and decomposition 有限代数的图：最大性、矩形性和分解

IF 0.6 4区数学

Algebra Universalis Pub Date : 2024-10-15 DOI: 10.1007/s00012-024-00874-4

Andrei A. Bulatov

引用次数: 0

Universal slices of the category of graphs 图类的普遍切片