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Absolute Indiscernibility 绝对不可辨认性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-04-29 DOI: 10.1007/s10469-025-09783-4
K. Zh. Kudaibergenov
{"title":"Absolute Indiscernibility","authors":"K. Zh. Kudaibergenov","doi":"10.1007/s10469-025-09783-4","DOIUrl":"10.1007/s10469-025-09783-4","url":null,"abstract":"<p>We look into the question about conditions under which any permutation of an indiscernible subset of a model extends to an automorphism of the model.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"195 - 200"},"PeriodicalIF":0.4,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091074","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
Isomorphism of Atomless Boolean Algebras with Distinguished Ideals 具有杰出理想的无原子布尔代数的同构
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-04-29 DOI: 10.1007/s10469-025-09781-6
S. S. Goncharov, J. Xiang
{"title":"Isomorphism of Atomless Boolean Algebras with Distinguished Ideals","authors":"S. S. Goncharov,&nbsp;J. Xiang","doi":"10.1007/s10469-025-09781-6","DOIUrl":"10.1007/s10469-025-09781-6","url":null,"abstract":"<p>An algebraic, model-theoretic, and algorithmic theory of enriched Boolean algebras with distinguished ideals was developed in a series of papers by D. E. Pal’chunov, A. Touraille, P. E. Alaev, N. T. Kogabaev, and other authors. Here we study the problem on the number of countable Boolean algebras with distinguished ideals for the case when an algebra and its quotient with respect to a distinguished ideal are atomless. It is proved that, for this subclass, there exist continuum many such countable structures.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"179 - 185"},"PeriodicalIF":0.4,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091163","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
Sessions of the Seminar “Algebra i Logika” “代数与逻辑学”研讨会分会场
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-04-29 DOI: 10.1007/s10469-025-09787-0
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-025-09787-0","DOIUrl":"10.1007/s10469-025-09787-0","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"232 - 234"},"PeriodicalIF":0.4,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091164","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
Duality for Bi-Algebraic Lattices Belonging to the Variety of (0, 1)-Lattices Generated by the Pentagon 属于五边形生成的(0,1)-格的双代数格的对偶性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-01-31 DOI: 10.1007/s10469-025-09776-3
W. Dziobiak, M. V. Schwidefsky
{"title":"Duality for Bi-Algebraic Lattices Belonging to the Variety of (0, 1)-Lattices Generated by the Pentagon","authors":"W. Dziobiak,&nbsp;M. V. Schwidefsky","doi":"10.1007/s10469-025-09776-3","DOIUrl":"10.1007/s10469-025-09776-3","url":null,"abstract":"<p>According to G. Birkhoff, there is a categorical duality between the category of bi-algebraic distributive (0, 1)-lattices with complete (0, 1)-lattice homomorphisms as morphisms and the category of partially ordered sets with partial order-preserving maps as morphisms. We extend this classical result to the bi-algebraic lattices belonging to the variety of (0, 1)-lattices generated by the pentagon, the 5-element nonmodular lattice. Applying the extended duality, we prove that the lattice of quasivarieties contained in the variety of (0, 1)-lattices generated by the pentagon has uncountably many elements and is not distributive. This yields the following: the lattice of quasivarieties contained in a nontrivial variety of (0, 1)-lattices either is a 2-element chain or has uncountably many elements and is not distributive.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 2","pages":"114 - 140"},"PeriodicalIF":0.4,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109883","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
Products of Quandles 昆德的产品
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-01-23 DOI: 10.1007/s10469-025-09773-6
V. G. Bardakov, D. A. Fedoseev
{"title":"Products of Quandles","authors":"V. G. Bardakov,&nbsp;D. A. Fedoseev","doi":"10.1007/s10469-025-09773-6","DOIUrl":"10.1007/s10469-025-09773-6","url":null,"abstract":"<p>We generalize the constructions of <i>Q</i>- and <i>G</i>-families of quandles introduced in the paper of A. Ishii et al. in [Ill. J. Math., <b>57</b>, No. 3, 817-838 (2013)], and establish how they are related to other constructions of quandles. A composition of structures of quandles defined on the same set is specified, and conditions are found under which this composition yields a quandle. It is proved that under such a multiplication we obtain a group that will be Abelian. Also a direct product of quandles is examined.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 2","pages":"75 - 97"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143107988","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
Periodic Groups Saturated with Finite Simple Symplectic Groups 饱和有限单辛群的周期群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-01-22 DOI: 10.1007/s10469-025-09774-5
Zh. Wang, W. Guo, D. V. Lytkina, V. D. Mazurov
{"title":"Periodic Groups Saturated with Finite Simple Symplectic Groups","authors":"Zh. Wang,&nbsp;W. Guo,&nbsp;D. V. Lytkina,&nbsp;V. D. Mazurov","doi":"10.1007/s10469-025-09774-5","DOIUrl":"10.1007/s10469-025-09774-5","url":null,"abstract":"<p>We study periodic groups saturated with finite simple symplectic groups.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 2","pages":"98 - 104"},"PeriodicalIF":0.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108905","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
Characterization of the Group A5 × A5 × A5 by the Set of Conjugacy Class Sizes 共轭类大小集对群A5 × A5 × A5的表征
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-01-22 DOI: 10.1007/s10469-025-09775-4
I. B. Gorshkov, V. V. Panshin
{"title":"Characterization of the Group A5 × A5 × A5 by the Set of Conjugacy Class Sizes","authors":"I. B. Gorshkov,&nbsp;V. V. Panshin","doi":"10.1007/s10469-025-09775-4","DOIUrl":"10.1007/s10469-025-09775-4","url":null,"abstract":"<p>For a finite group<i> G</i>, we denote by <i>N</i> (<i>G</i>) the set of its conjugacy class sizes. Recently, the following question was posed: given any <i>n</i> ∈ ℕ and an arbitrary non-Abelian finite simple group <i>S</i>, is it true that <i>G</i> ≃<i> S</i><sup><i>n</i></sup> if <i>G</i> is a group with trivial center and <i>N</i> (<i>G</i>) = <i>N</i> (<i>S</i><sup><i>n</i></sup>)? The answer to this question is known for all simple groups <i>S</i> with <i>n =</i> 1, and also for <i>S</i> ∈ {<i>A</i><sub>5</sub>, <i>A</i><sub>6</sub>}, where <i>A</i><sub><i>k</i></sub> denotes the alternating group of degree <i>k</i>, with <i>n</i> = 2. It is proved that the group <i>A</i><sub>5</sub> ×<i> A</i><sub>5</sub> ×<i> A</i><sub>5</sub> is uniquely defined by the set<i> N</i> (<i>A</i><sub>5</sub> ×<i> A</i><sub>5</sub> ×<i> A</i><sub>5</sub>) in the class of finite groups with trivial center.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 2","pages":"105 - 113"},"PeriodicalIF":0.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108906","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
Permutation Groups and Ideals of Turing Degrees 图灵度的置换群与理想
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-01-22 DOI: 10.1007/s10469-025-09777-2
A. S. Morozov, V. G. Puzarenko, M. Kh. Faizrakhmanov
{"title":"Permutation Groups and Ideals of Turing Degrees","authors":"A. S. Morozov,&nbsp;V. G. Puzarenko,&nbsp;M. Kh. Faizrakhmanov","doi":"10.1007/s10469-025-09777-2","DOIUrl":"10.1007/s10469-025-09777-2","url":null,"abstract":"<p>We study degrees and degree spectra of groups <span>({mathfrak{G}}_{mathrm{I}})</span> defined on a set of permutations of the natural numbers <i>ω</i> whose degrees belong to a Turing ideal I. A necessary condition and a sufficient condition are stated which specify whether an arbitrary Turing degree belongs to the degree spectrum of a group <span>({mathfrak{G}}_{mathrm{I}})</span>. Nonprincipal ideals I for which the group <span>({mathfrak{G}}_{mathrm{I}})</span> has or does not have a degree are exemplified.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 2","pages":"141 - 152"},"PeriodicalIF":0.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108999","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
Sessions of the Seminar “Algebra i Logika” “代数与逻辑学”研讨会分会场
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-01-16 DOI: 10.1007/s10469-025-09778-1
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-025-09778-1","DOIUrl":"10.1007/s10469-025-09778-1","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 2","pages":"153 - 154"},"PeriodicalIF":0.4,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108495","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
Nonmatrix Varieties of Nonassociative Algebras 非结合代数的非矩阵变异
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2024-12-23 DOI: 10.1007/s10469-024-09763-0
I. P. Shestakov, V. S. Bittencourt
{"title":"Nonmatrix Varieties of Nonassociative Algebras","authors":"I. P. Shestakov,&nbsp;V. S. Bittencourt","doi":"10.1007/s10469-024-09763-0","DOIUrl":"10.1007/s10469-024-09763-0","url":null,"abstract":"<p>A variety of associative algebras is nonmatrix if it does not contain the algebra of 2 × 2 matrices over a given field. Nonmatrix varieties were introduced and studied by V. N. Latyshev in [Algebra and Logic, <b>16</b>, No. 2, 98-122 (1977); Algebra and Logic, <b>16</b>, No. 2, 122-133 (1977); Mat. Zam., <b>27</b>, No. 1, 147-156 (1980)] in connection with the Specht problem. A series of equivalent characterizations of nonmatrix varieties was obtained in [Isr. J. Math., <b>181</b>, No. 1, 337-348 (2011)]. In the present paper, the notion of nonmatrix variety is extended to nonassociative algebras, and their characterization from the last-mentioned paper is generalized to alternative, Jordan, and some other varieties of algebras.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"62 6","pages":"532 - 547"},"PeriodicalIF":0.4,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889684","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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