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Sessions of the Seminar “Algebra i Logika” “代数与逻辑学”研讨会分会场
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-30 DOI: 10.1007/s10469-025-09794-1
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-025-09794-1","DOIUrl":"10.1007/s10469-025-09794-1","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"300 - 303"},"PeriodicalIF":0.6,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037111","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
CEA-Operators and the Ershov Hierarchy. II cea -算子和Ershov层次。2
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-28 DOI: 10.1007/s10469-025-09788-z
M. M. Arslanov, I. I. Batyrshin, M. M. Yamaleev
{"title":"CEA-Operators and the Ershov Hierarchy. II","authors":"M. M. Arslanov,&nbsp;I. I. Batyrshin,&nbsp;M. M. Yamaleev","doi":"10.1007/s10469-025-09788-z","DOIUrl":"10.1007/s10469-025-09788-z","url":null,"abstract":"<p>We continue and finalize our research started in [Algebra and Logic, <b>63</b>, No. 3 (2024), 168–178]. It is proved that there exists a noncomputable low c.e. set <i>A</i> such that any set that is <i>CEA</i>(<i>A</i>) and 2-c.e. has a c.e. degree.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"235 - 248"},"PeriodicalIF":0.6,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037397","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 Gelfand–Kirillov Conjecture as a First-Order Formula 一阶公式的Gelfand-Kirillov猜想
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-26 DOI: 10.1007/s10469-025-09792-3
H. L. Mariano, J. Schwarz
{"title":"The Gelfand–Kirillov Conjecture as a First-Order Formula","authors":"H. L. Mariano,&nbsp;J. Schwarz","doi":"10.1007/s10469-025-09792-3","DOIUrl":"10.1007/s10469-025-09792-3","url":null,"abstract":"<p>We show that for a given (reduced) root system Σ and for any algebraically closed field k with zero characteristic, the validity of the Gelfand–Kirillov conjecture for the finite-dimensional Lie algebra <span>({mathfrak{g}}_{mathrm{k},Sigma },)</span> the sole semisimple Lie algebra over k with root system Σ, is equivalent to the provability of a certain first-order sentence in the language of rings <span>(mathcal{L})</span>(0, 1, +, ∗, −) in the theory ACF<sub>0</sub> of algebraically closed fields of zero characteristic.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"284 - 293"},"PeriodicalIF":0.6,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037317","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
Generalized Baumslag–Solitar Groups Universally Equivalent to Tree Groups 广义baumslag -孤子群普遍等价于树群
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-08-26 DOI: 10.1007/s10469-025-09790-5
F. A. Dudkin
{"title":"Generalized Baumslag–Solitar Groups Universally Equivalent to Tree Groups","authors":"F. A. Dudkin","doi":"10.1007/s10469-025-09790-5","DOIUrl":"10.1007/s10469-025-09790-5","url":null,"abstract":"<p>A finitely generated group that acts on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group (<i>GBS</i> group). Every <i>GBS</i> group is the fundamental group <i>π</i><sub>1</sub>(𝔸) of a suitable labeled graph 𝔸. If 𝔸 is a labeled tree, then we call <i>π</i><sub>1</sub>(𝔸) a tree GBS group. It is known that <i>GBS</i> groups isomorphic to tree groups are themselves tree groups. It is shown that <i>GBS</i> groups universally equivalent to tree groups do not have to be tree groups. Moreover, we give a description of all <i>GBS</i> groups that are universally equivalent to tree groups.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 4","pages":"249 - 257"},"PeriodicalIF":0.6,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037316","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
Locally Finite Groups Containing Direct Products of Dihedral Groups 含二面体群的直积的局部有限群
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-14 DOI: 10.1007/s10469-025-09785-2
A. A. Shlepkin
{"title":"Locally Finite Groups Containing Direct Products of Dihedral Groups","authors":"A. A. Shlepkin","doi":"10.1007/s10469-025-09785-2","DOIUrl":"10.1007/s10469-025-09785-2","url":null,"abstract":"<p>We prove the theorem stating the following. Let <i>G</i> be a locally finite group saturated with groups from a set 𝔐 consisting of direct products of <i>d</i> dihedral groups. Then <i>G</i> is a direct product of d groups of the form <i>B</i> ⋋ &lt;υ&gt;, where <i>B</i> is a locally cyclic group inverted by an involution υ.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"217 - 227"},"PeriodicalIF":0.4,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091051","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
Decidable Models of Ehrenfeucht Theories 埃伦费希理论的可决定模型
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-05 DOI: 10.1007/s10469-025-09779-0
P. E. Alaev, E. I. Khlestova
{"title":"Decidable Models of Ehrenfeucht Theories","authors":"P. E. Alaev,&nbsp;E. I. Khlestova","doi":"10.1007/s10469-025-09779-0","DOIUrl":"10.1007/s10469-025-09779-0","url":null,"abstract":"<p>We study countable models of Ehrenfeucht theories, i.e., complete theories with a finite number of countable models, strictly larger than 1. The notion of a primely generated model is introduced. It is proved that if all complete types of an Ehrenfeucht theory have arithmetic complexity, then any of the primely generated models of the theory possesses an arithmetically complex isomorphic presentation.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"155 - 163"},"PeriodicalIF":0.4,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091032","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
Wielandt 𝔛 -Subgroups Wielandt𝔛-子组
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-03 DOI: 10.1007/s10469-025-09784-3
D. O. Revin
{"title":"Wielandt 𝔛 -Subgroups","authors":"D. O. Revin","doi":"10.1007/s10469-025-09784-3","DOIUrl":"10.1007/s10469-025-09784-3","url":null,"abstract":"<p>Let 𝔛 be a nonempty class of finite groups closed under taking subgroups, homomorphic images, and extensions. We define the concept of a Wielandt 𝔛 -subgroup in an arbitrary finite group. It generalizes the concept of a submaximal 𝔛 -subgroup introduced by H. Wielandt and is key in the framework of a program proposed by Wielandt in 1979. One of the central objectives of the program is to overcome difficulties associated with the reduction to factors of a subnormal series within the natural problem of searching for maximal 𝔛 -subgroups. Wielandt 𝔛 -subgroups possess a number of properties unshareable by submaximal 𝔛 -subgroups. There is a hope that, due to these additional properties, the use of Wielandt 𝔛 -subgroups will open up new possibilities in realizing Wielandt’s program.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"201 - 216"},"PeriodicalIF":0.4,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091018","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
CEA-Operators and the Ershov Hierarchy. I cea -算子和Ershov层次。我
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-02 DOI: 10.1007/s10469-025-09780-7
M. M. Arslanov, I. I. Batyrshin, M. M. Yamaleev
{"title":"CEA-Operators and the Ershov Hierarchy. I","authors":"M. M. Arslanov,&nbsp;I. I. Batyrshin,&nbsp;M. M. Yamaleev","doi":"10.1007/s10469-025-09780-7","DOIUrl":"10.1007/s10469-025-09780-7","url":null,"abstract":"<p>We consider the relationship between the CEA-hierarchy and the Ershov hierarchy in <span>({Delta }_{2}^{0})</span> Turing degrees. A degree <b>c</b> is called CEA(<b>a</b>) if <b>c</b> is computably enumerable in <b>a</b>, and <b>a</b> ≤ <b>c</b>. Soare and Stob [Stud. Logic Found. Math., <b>107</b>, 299-324 (1982)] proved that for a noncomputable low c.e. degree <b>a</b> there exists a CEA(<b>a</b>) degree that is not c.e. Later, Arslanov, Lempp, and Shore [Ann. Pure Appl. Logic, <b>78</b>, Nos. 1-3, 29-56 (1996)] formulated the problem of describing pairs of degrees <b>a</b> &lt; <b>e</b> such that there exists a CEA(<b>a</b>) 2-c.e. degree <b>d</b> ≤ <b>e</b> which is not c.e. Since then the question has remained open as to whether a CEA(<b>a</b>) degree in the sense of Soare and Stob can be made 2-c.e. Here we answer this question in the negative, solving it in a stronger formulation: there exists a noncomputable low c.e. degree <b>a</b> such that any CEA(<b>a</b>) ω-c.e. degree is c.e. Also possible generalizations of the result obtained are discussed, as well as various issues associated with the problem mentioned.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"164 - 178"},"PeriodicalIF":0.4,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091015","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
Connected Pseudofinite Unars 连通的伪有限元
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-05-01 DOI: 10.1007/s10469-025-09782-5
E. L. Efremov, A. A. Stepanova, S. G. Chekanov
{"title":"Connected Pseudofinite Unars","authors":"E. L. Efremov,&nbsp;A. A. Stepanova,&nbsp;S. G. Chekanov","doi":"10.1007/s10469-025-09782-5","DOIUrl":"10.1007/s10469-025-09782-5","url":null,"abstract":"<p>We start studying the structure of pseudofinite unars. Necessary (sufficient) conditions of being pseudofinite are formulated for connected unars without cycles, containing no chains, and we give examples showing that these conditions are not sufficient (resp. necessary). It is noted that a coproduct of chains is a pseudofinite unar; in particular, a chain is a pseudofinite unar. A nonpseudofinite unar without cycles, containing exactly one chain is exemplified. For connected unars without cycles, containing two chains, we formulate a necessary condition of being pseudofinite and give an example of a nonpseudofinite unar.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"186 - 194"},"PeriodicalIF":0.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090989","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
Punctual Spectra of Algebraic Structures and Isomorphisms 代数结构和同构的准时谱
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2025-04-30 DOI: 10.1007/s10469-025-09786-1
N. A. Bazhenov, I. Sh. Kalimullin
{"title":"Punctual Spectra of Algebraic Structures and Isomorphisms","authors":"N. A. Bazhenov,&nbsp;I. Sh. Kalimullin","doi":"10.1007/s10469-025-09786-1","DOIUrl":"10.1007/s10469-025-09786-1","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 3","pages":"228 - 231"},"PeriodicalIF":0.4,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144091193","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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