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Construction of a Nilsemigroup of Paths in a Countable Family of Uniformly Elliptic Complexes 一致椭圆配合物可数族中nili半群路径的构造
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-11-11 DOI: 10.1007/s10469-025-09803-3
I. A. Ivanov-Pogodaev, A. Ya. Kanel-Belov
{"title":"Construction of a Nilsemigroup of Paths in a Countable Family of Uniformly Elliptic Complexes","authors":"I. A. Ivanov-Pogodaev,&nbsp;A. Ya. Kanel-Belov","doi":"10.1007/s10469-025-09803-3","DOIUrl":"10.1007/s10469-025-09803-3","url":null,"abstract":"<p>The paper is devoted to the construction of a finitely presented infinite nilsemigroup satisfying the identity <i>x</i><sup>9</sup> = 0. We describe an algorithm reducing arbitrary semigroup words to a canonical form. We prove that any word containing a subword of period 9 can be reduced to zero using the defining relations. At the same time, there exist words corresponding to arbitrarily long paths whose length does not decrease, demonstrating that the constructed semigroup is infinite.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 6","pages":"410 - 438"},"PeriodicalIF":0.6,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533360","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
Every Nonzero Enumeration Degree Contains Infinitely Many Singleton Degrees 每个非零枚举度包含无限多个单态度
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-11-10 DOI: 10.1007/s10469-025-09804-2
T. F. Kent, K. M. Ng, A. Sorbi
{"title":"Every Nonzero Enumeration Degree Contains Infinitely Many Singleton Degrees","authors":"T. F. Kent,&nbsp;K. M. Ng,&nbsp;A. Sorbi","doi":"10.1007/s10469-025-09804-2","DOIUrl":"10.1007/s10469-025-09804-2","url":null,"abstract":"<p>Extending a result of Zacharov, we show that every nonzero enumeration degree consists of infinitely many s-degrees. In fact, we show that there is no minimal s-degree inside any nonzero enumeration degree. This answers open questions in the literature raised by Cooper and Batyrshin.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 6","pages":"439 - 447"},"PeriodicalIF":0.6,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533358","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
Mappings with Coenumerable Graphs 具有可枚举图的映射
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-11-04 DOI: 10.1007/s10469-025-09805-1
A. S. Morozov
{"title":"Mappings with Coenumerable Graphs","authors":"A. S. Morozov","doi":"10.1007/s10469-025-09805-1","DOIUrl":"10.1007/s10469-025-09805-1","url":null,"abstract":"<p>We study partial mappings on natural numbers, the graphs of which are coenumerable. Such mappings are referred to as negative mappings. We show that any <b>0′</b>-computable partial function is represented as the superposition of two negative ones. We also show that the inverse semigroup of all <b>0′</b>-computable partial injective mappings is generated by its negative elements; moreover, any its element is equal to the product of its two negative elements. We show that the group of all <b>0′</b>-computable permutations is generated by its negative elements. We obtain sufficient conditions for the representability of <b>0′</b>- computable permutations in the form of the superposition of two negative permutations.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 6","pages":"448 - 457"},"PeriodicalIF":0.6,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533355","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
Cohomologies of Some Four-Dimensional Simple Jordan Superalgebras 一些四维简单Jordan超代数的上同调
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-11-03 DOI: 10.1007/s10469-025-09806-0
J. A. Ramírez-Bermúdez, F. A. Gómez-González
{"title":"Cohomologies of Some Four-Dimensional Simple Jordan Superalgebras","authors":"J. A. Ramírez-Bermúdez,&nbsp;F. A. Gómez-González","doi":"10.1007/s10469-025-09806-0","DOIUrl":"10.1007/s10469-025-09806-0","url":null,"abstract":"<p>We calculate the second cohomology group for the four-dimensional simple Jordan superalgebra 𝒥osp<sub>1|2</sub>(𝔽) by proving that its second cohomology group with coefficients in the regular representation is isomorphic to <span>({mathbb{F}}dot{+}0)</span>. We show (without proof) that for the four-dimensional simple Jordan superalgebra 𝒟<sub><i>t</i></sub> with <i>t</i> ≠ 0, the superalgebra (<i>V</i>, <i>f</i>) of a superform with <i>n</i> = 1 and <i>m</i> = 1, and ℳ<sub>1|1</sub>(𝔽)<sup>(+)</sup> the respective second cohomology groups (with coefficients in the regular representation) are isomorphic to <span>({mathbb{F}}dot{+}0)</span>.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 6","pages":"458 - 474"},"PeriodicalIF":0.6,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533356","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 2-Decidability of Boolean Algebras with One Distinguished Ideal 具有一个杰出理想的布尔代数的2-可判定性
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-10-31 DOI: 10.1007/s10469-025-09802-4
M. N. Gaskova
{"title":"The 2-Decidability of Boolean Algebras with One Distinguished Ideal","authors":"M. N. Gaskova","doi":"10.1007/s10469-025-09802-4","DOIUrl":"10.1007/s10469-025-09802-4","url":null,"abstract":"<p>We give a description of 2-decidable Boolean algebras with one distinguished ideal in terms of the computability of some set of predicates on a given algebra.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 6","pages":"399 - 409"},"PeriodicalIF":0.6,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533359","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
An Anick Type Wild Automorphism of Free Poisson Algebras 自由泊松代数的Anick型野生自同构
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-10-06 DOI: 10.1007/s10469-025-09799-w
I. P. Shestakov, Z. Zhang
{"title":"An Anick Type Wild Automorphism of Free Poisson Algebras","authors":"I. P. Shestakov,&nbsp;Z. Zhang","doi":"10.1007/s10469-025-09799-w","DOIUrl":"10.1007/s10469-025-09799-w","url":null,"abstract":"<p>We construct an Anick type wild automorphism in a 3-generated free Poisson algebra which induces a tame automorphism in a 3-generated polynomial algebra. We also show that this automorphism is stably tame.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 5","pages":"367 - 382"},"PeriodicalIF":0.6,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256486","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 Projective Spaces 射影空间的模型理论
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-10-06 DOI: 10.1007/s10469-025-09796-z
B. A. Berger, A. G. Myasnikov
{"title":"Model Theory of Projective Spaces","authors":"B. A. Berger,&nbsp;A. G. Myasnikov","doi":"10.1007/s10469-025-09796-z","DOIUrl":"10.1007/s10469-025-09796-z","url":null,"abstract":"<p>It is proved that, for any vector space V over a field f of finite dimension at least 3, the projective space P(V) (the set of all subspaces of V equpped with a binary predicate of inclusion) is regularly injectively bi-interpretable with the field F.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 5","pages":"323 - 348"},"PeriodicalIF":0.6,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256485","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
Completion of the Solvable Baumslag–Solitar group. Elementary Theory 完成可解的Baumslag-Solitar群。基本理论
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-29 DOI: 10.1007/s10469-025-09798-x
N. S. Romanovskii
{"title":"Completion of the Solvable Baumslag–Solitar group. Elementary Theory","authors":"N. S. Romanovskii","doi":"10.1007/s10469-025-09798-x","DOIUrl":"10.1007/s10469-025-09798-x","url":null,"abstract":"<p>For the solvable Baumslag–Solitar group BS(1, <i>n</i>) (<i>n</i> &gt; 1), we define the divisible completion BSd(1, <i>n</i>). We describe groups that are elementarily equivalent to the group BSd(1, <i>n</i>), find the axiomatics of the theory of the group BSd(1, <i>n</i>), and prove the decidability of this theory.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 5","pages":"355 - 366"},"PeriodicalIF":0.6,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256737","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
Mal’tsev Correspondence and Bi-Interpretability 马尔采夫对应和双可解释性
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-24 DOI: 10.1007/s10469-025-09795-0
M. G. Amaglobeli, T. Z. Bokelavadze, A. G. Myasnikov
{"title":"Mal’tsev Correspondence and Bi-Interpretability","authors":"M. G. Amaglobeli,&nbsp;T. Z. Bokelavadze,&nbsp;A. G. Myasnikov","doi":"10.1007/s10469-025-09795-0","DOIUrl":"10.1007/s10469-025-09795-0","url":null,"abstract":"<p>We study the famous Mal’tsev correspondence between nilpotent <i>k</i>-groups <i>G</i> and nilpotent Lie <i>k</i>-algebras <i>L</i> over a field <i>k</i> of characteristic zero from the model-theoretic, algebro-geometric, and algorithmic viewpoints. It is proved that, in this case, a group <i>G</i> and the corresponding Lie algebra <i>L</i>(<i>G</i>) are bi-interpretable by equations in each other. This gives a much more precise description of the correspondence, which implies that, in addition to the classical categorical properties, the group <i>G</i> and the algebra <i>L</i>(<i>G</i>) share many more algebraic, algorithmic, and model-theoretic properties.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 5","pages":"305 - 322"},"PeriodicalIF":0.6,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256825","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
Finite Symmetric Groups are Strongly Verbally Closed 有限对称群是强语言闭群
IF 0.6 3区 数学
Algebra and Logic Pub Date : 2025-09-23 DOI: 10.1007/s10469-025-09797-y
O. K. Karimova, A. A. Klyachko
{"title":"Finite Symmetric Groups are Strongly Verbally Closed","authors":"O. K. Karimova,&nbsp;A. A. Klyachko","doi":"10.1007/s10469-025-09797-y","DOIUrl":"10.1007/s10469-025-09797-y","url":null,"abstract":"<p>Answering a question of A. V. Vasil’ev, we show that each finite symmetric (or alternating) group H is a retract of any group containing H as a verbally closed subgroup.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"63 5","pages":"349 - 354"},"PeriodicalIF":0.6,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256797","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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