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The Homology of the Lamplighter Lie Algebra Lamplier李代数的同调
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2022-05-16 DOI: 10.1007/s10469-022-09668-w
Y. Félix, A. Murillo
{"title":"The Homology of the Lamplighter Lie Algebra","authors":"Y. Félix,&nbsp;A. Murillo","doi":"10.1007/s10469-022-09668-w","DOIUrl":"10.1007/s10469-022-09668-w","url":null,"abstract":"<div><div><p>It is proved that the associated Lie algebra of the Mal’tsev ℚ-completion of the lamplighter group is the pronilpotent completion of the lamplighter Lie algebra. It is also shown that the homology of this completed Lie algebra is of uncountable dimension in each degree.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"425 - 432"},"PeriodicalIF":0.5,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50488117","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: 2
Fields of Algebraic Numbers Computable in Polynomial Time. II 多项式时间可计算代数数的域。二、
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2022-05-06 DOI: 10.1007/s10469-022-09661-3
P. E. Alaev, V. L. Selivanov
{"title":"Fields of Algebraic Numbers Computable in Polynomial Time. II","authors":"P. E. Alaev,&nbsp;V. L. Selivanov","doi":"10.1007/s10469-022-09661-3","DOIUrl":"10.1007/s10469-022-09661-3","url":null,"abstract":"<div><div><p>This paper is a continuation of [Algebra and Logic, 58, No. 6, 447-469 (2019)] where we constructed polynomial-time presentations for the field of complex algebraic numbers and for the ordered field of real algebraic numbers. Here we discuss other known natural presentations of such structures. It is shown that all these presentations are equivalent to each other and prove a theorem which explains why this is so. While analyzing the presentations mentioned, we introduce the notion of a quotient structure. It is shown that the question whether a polynomial-time computable quotient structure is equivalent to an ordinary one is almost equivalent to the P = NP problem. Conditions are found under which the answer is positive.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"349 - 359"},"PeriodicalIF":0.5,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50456783","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: 2
Groups Saturated with Finite Frobenius Groups with Complements of Even Order 偶数阶补的有限Frobenius群饱和群
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2022-05-05 DOI: 10.1007/s10469-022-09664-0
B. E. Durakov
{"title":"Groups Saturated with Finite Frobenius Groups with Complements of Even Order","authors":"B. E. Durakov","doi":"10.1007/s10469-022-09664-0","DOIUrl":"10.1007/s10469-022-09664-0","url":null,"abstract":"<div><div><p>We prove a theorem stating the following. Let G be a periodic group saturated with finite Frobenius groups with complements of even order, and let i be an involution of G. If, for some elements a, b ∈ G with the condition |a| · |b| &gt; 4, all subgroups 〈<i>a</i>, <i>b</i><sup><i>g</i></sup>〉, where g ∈ G, are finite, then G = A λ C<sub>G</sub>(i) is a Frobenius group with Abelian kernel A and complement C<sub>G</sub>(i) whose elementary Abelian subgroups are all cyclic.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"375 - 379"},"PeriodicalIF":0.5,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50454099","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: 1
Virtual Algebraic Isomorphisms between Predicate Calculi of Finite Rich Signatures 有限富特征谓词演算之间的虚拟代数同构
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2022-05-03 DOI: 10.1007/s10469-022-09666-y
M. G. Peretyat’kin
{"title":"Virtual Algebraic Isomorphisms between Predicate Calculi of Finite Rich Signatures","authors":"M. G. Peretyat’kin","doi":"10.1007/s10469-022-09666-y","DOIUrl":"10.1007/s10469-022-09666-y","url":null,"abstract":"<div><div><p>It is proved that every two predicate calculi of finite rich signatures are algebraically virtually isomorphic, i.e., some of their Cartesian extensions are algebraically isomorphic. As an important application, it is stated that for predicate calculi in any two finite rich signatures, there exists a computable isomorphism between their Tarski–Lindenbaum algebras which preserves all model-theoretic properties of algebraic type corresponding to the real practice of research in model theory.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"389 - 406"},"PeriodicalIF":0.5,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50446292","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 with Dense Spectrum 具有稠密谱的周期群
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2022-04-29 DOI: 10.1007/s10469-022-09669-9
A. S. Mamontov
{"title":"Periodic Groups with Dense Spectrum","authors":"A. S. Mamontov","doi":"10.1007/s10469-022-09669-9","DOIUrl":"10.1007/s10469-022-09669-9","url":null,"abstract":"<div><div><p>Presented by the Dissertation Council D 003.015.02</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"433 - 439"},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50522192","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 Being Equivalent to Horn Formulas Horn公式等价问题的复杂性
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2022-04-29 DOI: 10.1007/s10469-022-09665-z
N. T. Kogabaev
{"title":"Complexity of the Problem of Being Equivalent to Horn Formulas","authors":"N. T. Kogabaev","doi":"10.1007/s10469-022-09665-z","DOIUrl":"10.1007/s10469-022-09665-z","url":null,"abstract":"<div><div><p>We look at the complexity of the existence problem for a Horn sentence (identity, quasi-identity, ∀-sentence, ∃-sentence) equivalent to a given one. It is proved that if the signature contains at least one symbol of arity k ≥ 2, then each of the problems mentioned is an m-complete <span>( {Sigma}_1^0 )</span> set.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"380 - 388"},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50522194","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: 1
Modal Bilattice Logic and its Extensions 模态双格逻辑及其扩展
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2022-04-29 DOI: 10.1007/s10469-022-09667-x
S. O. Speranski
{"title":"Modal Bilattice Logic and its Extensions","authors":"S. O. Speranski","doi":"10.1007/s10469-022-09667-x","DOIUrl":"10.1007/s10469-022-09667-x","url":null,"abstract":"<div><div><p>We consider the lattices of extensions of three logics: (1) modal bilattice logic; (2) full Belnap–Dunn bimodal logic; (3) classical bimodal logic. It is proved that these lattices are isomorphic to each other. Furthermore, the isomorphisms constructed preserve various nice properties, such as tabularity, pretabularity, decidability or Craig’s interpolation property.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"407 - 424"},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50522193","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i Logika”研讨会
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2022-04-29 DOI: 10.1007/s10469-022-09670-2
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-022-09670-2","DOIUrl":"10.1007/s10469-022-09670-2","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 6","pages":"440 - 441"},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50522191","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
Algebras of Distributions of Binary Isolating Formulas for Almost ω-Categorical Weakly o-Minimal Theories 几乎ω-范畴弱o-极小理论的二元隔离公式的分布代数
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2021-12-03 DOI: 10.1007/s10469-021-09650-y
A. B. Altayeva, B. Sh. Kulpeshov, S. V. Sudoplatov
{"title":"Algebras of Distributions of Binary Isolating Formulas for Almost ω-Categorical Weakly o-Minimal Theories","authors":"A. B. Altayeva,&nbsp;B. Sh. Kulpeshov,&nbsp;S. V. Sudoplatov","doi":"10.1007/s10469-021-09650-y","DOIUrl":"10.1007/s10469-021-09650-y","url":null,"abstract":"<div><div><p>We describe distribution algebras of binary isolating formulas over 1-type for almost <i>ω</i>-categorical weakly <i>o</i>-minimal theories. It is proved that an isomorphism of these algebras for two 1-types is characterized by the coincidence of binary convexity ranks, as well as by the simultaneous fulfillment of isolation, quasirationality or irrationality of the two types. A criterion is established for an algebra of formulas over a pair of not weakly orthogonal 1-types to be generalized commutative for almost <i>ω</i>-categorical weakly <i>o</i>-minimal theories.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 4","pages":"241 - 262"},"PeriodicalIF":0.5,"publicationDate":"2021-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50444910","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: 2
T1-Separable Numberings of Subdirectly Indecomposable Algebras 次直不可分解代数的T1可分数
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2021-12-03 DOI: 10.1007/s10469-021-09651-x
N. Kh. Kasymov, A. S. Morozov, I. A. Khodzhamuratova
{"title":"T1-Separable Numberings of Subdirectly Indecomposable Algebras","authors":"N. Kh. Kasymov,&nbsp;A. S. Morozov,&nbsp;I. A. Khodzhamuratova","doi":"10.1007/s10469-021-09651-x","DOIUrl":"10.1007/s10469-021-09651-x","url":null,"abstract":"<div><div><p>We prove the existence of a natural subclass of subdirectly indecomposable algebras all of whose Hausdorff numberings are negative. We also construct a <i>T</i><sub>1</sub>-separable nonnegative subdirectly indecomposable algebra with Artinian congruence lattice.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"60 4","pages":"263 - 278"},"PeriodicalIF":0.5,"publicationDate":"2021-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50444911","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: 1
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