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Chiral Algebras with Abelian Conformal Part 具有阿贝尔保角部分的手性代数
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-10-20 DOI: 10.1007/s10469-026-09853-1
I. V. Dudin, P. S. Kolesnikov
{"title":"Chiral Algebras with Abelian Conformal Part","authors":"I. V. Dudin,&nbsp;P. S. Kolesnikov","doi":"10.1007/s10469-026-09853-1","DOIUrl":"10.1007/s10469-026-09853-1","url":null,"abstract":"<p>We study a categorical approach to the concept of varieties of chiral algebras. We prove that the class of chiral algebras in the variety defined by a binary quadratic operad Var, whose conformal structure is abelian, coincides with the class of differential algebras in the variety defined by the Manin black product of the operads Var and Com, where Com is the operad of associative commutative algebras.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"65 1","pages":"30 - 51"},"PeriodicalIF":0.4,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149250449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Index Sets of Decidably Categorical Models with Unary Functional Symbols 一元函数符号的可决范畴模型的指标集
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-10-15 DOI: 10.1007/s10469-026-09850-4
N. A. Bazhenov, M. I. Marchuk
{"title":"Index Sets of Decidably Categorical Models with Unary Functional Symbols","authors":"N. A. Bazhenov,&nbsp;M. I. Marchuk","doi":"10.1007/s10469-026-09850-4","DOIUrl":"10.1007/s10469-026-09850-4","url":null,"abstract":"<p>We obtain a criterion for decidable categoricity of injective unars. Exact complexity estimates are established for the index sets of the classes of strongly constructivizable injective unars and decidably categorical injective unars. It is shown that the index set of decidably categorical structures in a signature consisting of two unary functional symbols is <span>({Sigma}_{omega +2}^{0})</span>-complete.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"65 1","pages":"10 - 20"},"PeriodicalIF":0.4,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149250648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On Unions of Chains of Jónsson Algebras Jónsson代数链的并集
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-10-15 DOI: 10.1007/s10469-026-09855-z
K. Zh. Kudaibergenov
{"title":"On Unions of Chains of Jónsson Algebras","authors":"K. Zh. Kudaibergenov","doi":"10.1007/s10469-026-09855-z","DOIUrl":"10.1007/s10469-026-09855-z","url":null,"abstract":"<p>Some conditions are given under which the union of an increasing chain of Jónsson algebras is again a Jónsson algebra. Conditions are found under which there exists a countable increasing chain of Jónsson groups whose union is not a Jónsson group.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"65 1","pages":"64 - 68"},"PeriodicalIF":0.4,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149250645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Complexity of the Problem of ∀-Representability for Sentences in Signatures with Unary Symbols 一元符号签名中句子的∀-可表示性问题的复杂性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-10-15 DOI: 10.1007/s10469-026-09854-0
N. T. Kogabaev
{"title":"Complexity of the Problem of ∀-Representability for Sentences in Signatures with Unary Symbols","authors":"N. T. Kogabaev","doi":"10.1007/s10469-026-09854-0","DOIUrl":"10.1007/s10469-026-09854-0","url":null,"abstract":"<p>We study the complexity of the existence problem of a ∀-sentence (∃-sentence) equivalent to a given sentence in signatures containing only unary symbols. We prove that if the signature consists of an at most one function symbol and an arbitrary number of predicate symbols, then both these problems are computable. If the signature contains at least two function symbols and arbitrarily many predicate symbols, we establish that each of these problems is an <i>m</i>-complete <span>({Sigma}_{1}^{0})</span>-set.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"65 1","pages":"52 - 63"},"PeriodicalIF":0.4,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149250646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Arithmetic Invariants for Finite Simple and Related Groups 有限单群及相关群的算术不变量
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-10-15 DOI: 10.1007/s10469-026-09851-3
A. V. Vasil’ev
{"title":"Arithmetic Invariants for Finite Simple and Related Groups","authors":"A. V. Vasil’ev","doi":"10.1007/s10469-026-09851-3","DOIUrl":"10.1007/s10469-026-09851-3","url":null,"abstract":"<p>In this short note, we address problems concerning the characterization of simple and related groups by various arithmetic invariants. We propose a uniform approach to such questions and discuss both known results and open problems in this area.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"65 1","pages":"21 - 29"},"PeriodicalIF":0.4,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149250647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Element Orders in the Graph Automorphism Extensions of Finite Linear and Unitary Groups in Characteristic Two 特征2有限线性酉群图自同构扩展中的元素阶
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-10-14 DOI: 10.1007/s10469-026-09852-2
S. S. Saidov
{"title":"Element Orders in the Graph Automorphism Extensions of Finite Linear and Unitary Groups in Characteristic Two","authors":"S. S. Saidov","doi":"10.1007/s10469-026-09852-2","DOIUrl":"10.1007/s10469-026-09852-2","url":null,"abstract":"<p>We study element orders in the graph automorphism extensions of finite linear and unitary groups in characteristic two.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"65 1","pages":"69 - 78"},"PeriodicalIF":0.4,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149250763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Abstract Algorithmic Classes 抽象算法类
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-10-13 DOI: 10.1007/s10469-026-09849-x
P. E. Alaev
{"title":"Abstract Algorithmic Classes","authors":"P. E. Alaev","doi":"10.1007/s10469-026-09849-x","DOIUrl":"10.1007/s10469-026-09849-x","url":null,"abstract":"<p>We consider several approaches to defining an abstract algorithmic class formulated in the language of operators. We give conditions under which standard algorithmic classes have the introduced properties. Several examples of algebraic constructions that preserve algorithmic classes are given.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"65 1","pages":"1 - 9"},"PeriodicalIF":0.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149250556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Model Theory of Enriched Boolean Algebras 富布尔代数的模型理论
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-09-02 DOI: 10.1007/s10469-026-09846-0
D. E. Pal’chunov, A. V. Trofimov
{"title":"Model Theory of Enriched Boolean Algebras","authors":"D. E. Pal’chunov,&nbsp;A. V. Trofimov","doi":"10.1007/s10469-026-09846-0","DOIUrl":"10.1007/s10469-026-09846-0","url":null,"abstract":"<p>We study enriched Boolean algebras. We describe subalgebras of Boolean algebras determined by fixed elements of automorphisms. We construct a continuum of superatomic Boolean algebras with a distinguished subalgebra whose elementary theories have no prime model. We investigate semigroups of elementary types of Boolean algebras with a distinguished subalgebra and of Boolean algebras with distinguished ideals.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"435 - 446"},"PeriodicalIF":0.4,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On Unbounded Groups of Permutations of Natural Numbers 关于自然数置换的无界群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-08-28 DOI: 10.1007/s10469-026-09848-y
N. M. Suchkov, A. A. Shlyopkin
{"title":"On Unbounded Groups of Permutations of Natural Numbers","authors":"N. M. Suchkov,&nbsp;A. A. Shlyopkin","doi":"10.1007/s10469-026-09848-y","DOIUrl":"10.1007/s10469-026-09848-y","url":null,"abstract":"<p>Let <i>G</i> be the group of all bounded permutations of the set of natural numbers <span>({mathbb{N}})</span>. Suppose that a group <i>H</i> contains elements <i>h</i>, <i>h</i><sub>1</sub>, . . . , <i>h</i><sub><i>n</i></sub>, . . . such that |<i>h</i>| = ∞, <span>({h}_{1}^{p})</span> = <i>h</i>, <span>({h}_{2}^{p})</span> = <i>h</i><sub>1</sub>, . . . , <span>({h}_{n}^{p})</span> = <i>h</i><sub><i>n</i>−1</sub>, . . . , where <i>p</i> is a prime number. We prove that <i>H</i> is not isomorphic to a subgroup of <i>G</i>.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"455 - 461"},"PeriodicalIF":0.4,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Groups G2(2m) and 3D4(23m) as Automorphism Groups of Regular Polytopes of Rank 3, 4, and 5 群G2（2m）和3D4（23m）为3、4、5阶正多面体的自同构群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2026-08-28 DOI: 10.1007/s10469-026-09844-2
R. I. Gvozdev, Ya. N. Nuzhin
{"title":"The Groups G2(2m) and 3D4(23m) as Automorphism Groups of Regular Polytopes of Rank 3, 4, and 5","authors":"R. I. Gvozdev,&nbsp;Ya. N. Nuzhin","doi":"10.1007/s10469-026-09844-2","DOIUrl":"10.1007/s10469-026-09844-2","url":null,"abstract":"<p>We prove that <i>G</i><sub>2</sub>(2<sup><i>m</i></sup>) and <sup>3</sup><i>D</i><sub>4</sub>(2<sup>3<i>m</i></sup>) are automorphism groups of regular polytopes of rank<i> n</i> = 4, 5, except for the group <sup>3</sup><i>D</i><sub>4</sub>(2<sup>3<i>m</i></sup>) when <i>n</i> = 5 and m is a power of 3. The minimal number of generating conjugate involutions whose product equals 1 is found, and the existence of new regular polytopes of rank 3 with these automorphism groups is established.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"64 6","pages":"412 - 431"},"PeriodicalIF":0.4,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148909648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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