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Generic Complexity of the Word Problem in Some Semigroups 某些半群中字问题的一般复杂性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-11-15 DOI: 10.1007/s10469-023-09717-y
A. N. Rybalov
{"title":"Generic Complexity of the Word Problem in Some Semigroups","authors":"A. N. Rybalov","doi":"10.1007/s10469-023-09717-y","DOIUrl":"10.1007/s10469-023-09717-y","url":null,"abstract":"<p>Generic algorithms decide problems on sets of almost all inputs, outputting an indefinite answer for other rare inputs. We will prove that the word problem is generically decidable in finitely generated semigroups 𝔖, for which there exists a congruence <i>θ</i> such that the semigroup 𝔖/<i>θ</i> is an infinite residually finite monoid with cancellation property and decidable word problem. This generalizes the author’ earlier result on generic decidability of the word problem in finitely presented semigroups that remain infinite when adding commutativity and cancelling properties. Examples of such semigroups are one-relator semigroups as well as so-called balanced semigroups, for which generic decidability of the word problem has been proved by Won. In particular, balanced are Tseitin and Makanin’s classical semigroups with undecidable word problem.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 6","pages":"524 - 536"},"PeriodicalIF":0.4,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138529823","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
Structure of Singular Superalgebras with 2-Dimensional Even Part and New Examples of Singular Superalgebras 具有二维偶数部分的奇异超代数的结构和奇异超代数的新实例
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-11-08 DOI: 10.1007/s10469-023-09716-z
S. V. Pchelintsev, O. V. Shashkov
{"title":"Structure of Singular Superalgebras with 2-Dimensional Even Part and New Examples of Singular Superalgebras","authors":"S. V. Pchelintsev,&nbsp;O. V. Shashkov","doi":"10.1007/s10469-023-09716-z","DOIUrl":"10.1007/s10469-023-09716-z","url":null,"abstract":"<p>It is proved that a singular superalgebra with a 2-dimensional even part is isomorphic to a superalgebra <i>B</i><sub>2|3</sub>(φ<i>, ξ, ψ</i>)<i>.</i> In particular, there do not exist infinite-dimensional simple singular superalgebras with a 2-dimensional even part. It is proved that if a singular superalgebra contains an odd left annihilator, then it contains a nondegenerate switch. Lastly, it is established that for any number <i>N ≥</i> 5, except the numbers 6, 7, 8, 11, there exist singular superalgebras with a switch of dimension <i>N</i>. For the numbers<i> N</i> = 6, 7, 8, 11, there do not exist singular <i>N</i> -dimensional superalgebras with a switch.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 6","pages":"506 - 523"},"PeriodicalIF":0.4,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346370","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
Cardinality Reduction Theorem for Logics QHC and QH4 逻辑 QHC 和 QH4 的 Cardinality Reduction Theorem for Logics QHC 和 QH4
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-11-08 DOI: 10.1007/s10469-023-09715-0
A. A. Onoprienko
{"title":"Cardinality Reduction Theorem for Logics QHC and QH4","authors":"A. A. Onoprienko","doi":"10.1007/s10469-023-09715-0","DOIUrl":"10.1007/s10469-023-09715-0","url":null,"abstract":"<p>The joint logic of problems and propositions QHC introduced by S. A. Melikhov, as well as intuitionistic modal logic QH4, is studied. An immersion of these logics into classical first-order predicate logic is considered. An analog of the Löwenheim–Skolem theorem on the existence of countable elementary submodels for QHC and QH4 is established.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 6","pages":"491 - 505"},"PeriodicalIF":0.4,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135390235","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
A Class of Generalized Derivations 一类广义派生
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-11-03 DOI: 10.1007/s10469-023-09713-2
A. S. Zakharov
{"title":"A Class of Generalized Derivations","authors":"A. S. Zakharov","doi":"10.1007/s10469-023-09713-2","DOIUrl":"10.1007/s10469-023-09713-2","url":null,"abstract":"<p>We consider a class of generalized derivations that arise in connection with the problem of adjoining unity to an algebra with generalized derivation, and of searching envelopes for Novikov–Poisson algebras. Conditions for the existence of the localization of an algebra with ternary derivation are specified, as well as conditions under which given an algebra with ternary derivation, we can construct a Novikov–Poisson algebra and a Jordan superalgebra. Finally, we show how the simplicity of an algebra with Brešar generalized derivation is connected with simplicity of the appropriate Novikov algebra.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 6","pages":"466 - 480"},"PeriodicalIF":0.4,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135867992","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 "研讨会课程
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-11-02 DOI: 10.1007/s10469-023-09719-w
{"title":"Sessions of the Seminar “Algebra i Logika”","authors":"","doi":"10.1007/s10469-023-09719-w","DOIUrl":"10.1007/s10469-023-09719-w","url":null,"abstract":"","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 6","pages":"545 - 545"},"PeriodicalIF":0.4,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135933123","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 Stability of the Class of Injective S-Acts 注入式 S-行为类的广义稳定性
IF 0.4 3区 数学
Algebra and Logic Pub Date : 2023-11-01 DOI: 10.1007/s10469-023-09718-x
A. A. Stepanova
{"title":"Generalized Stability of the Class of Injective S-Acts","authors":"A. A. Stepanova","doi":"10.1007/s10469-023-09718-x","DOIUrl":"10.1007/s10469-023-09718-x","url":null,"abstract":"<p>The concept of P-stability is a particular case of generalized stability of complete theories. We study injective <i>S</i>-acts with a <i>P</i>-stable theory. It is proved that the class of injective <i>S</i>-acts is (<i>P</i>, 1)-stable only if <i>S</i> is a one-element monoid. Also we describe commutative and linearly ordered monoids <i>S</i> the class of injective <i>S</i>-acts over which is (<i>P</i>, <i>s</i>)-, (<i>P</i>, <i>a</i>)-, and (<i>P</i>, <i>e</i>)-stable.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 6","pages":"537 - 544"},"PeriodicalIF":0.4,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135321441","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
Modification and Correction of Medvedev’s Example of a Solvable Alternative Algebra 对Medvedev可解替代代数例子的修正
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-09-06 DOI: 10.1007/s10469-023-09709-y
I. P. Shestakov
{"title":"Modification and Correction of Medvedev’s Example of a Solvable Alternative Algebra","authors":"I. P. Shestakov","doi":"10.1007/s10469-023-09709-y","DOIUrl":"10.1007/s10469-023-09709-y","url":null,"abstract":"<div><div><p>Yu. A. Medvedev [Algebra and Logic, <b>19</b>, No. 3, 191—201 (1980)] constructed an example of alternative algebra that he used to prove that a certain variety of alternative algebras possess the non-Specht property over a field of characteristic 2. Though his result concerned the characteristic 2 case, the example was claimed to be alternative over an arbitrary field, and it was later used by V. T. Filippov in a series of papers. Unfortunately, Medvedev’s example is in fact not alternative in any characteristic. Therefore, whether the variety considered by Medvedev has the non-Specht property is still not clear. Moreover, the results of Filippov’s papers, in which Medvedev’s example was used, also become questionable. We construct new examples and employ them to prove that the results of Filippov remain true.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"420 - 436"},"PeriodicalIF":0.5,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50457125","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
Partial Hopf–Galois Theory 部分Hopf–Galois理论
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-09-04 DOI: 10.1007/s10469-023-09707-0
F. Castro, D. Freitas, A. Paques, G. Quadros, T. Tamusiunas
{"title":"Partial Hopf–Galois Theory","authors":"F. Castro,&nbsp;D. Freitas,&nbsp;A. Paques,&nbsp;G. Quadros,&nbsp;T. Tamusiunas","doi":"10.1007/s10469-023-09707-0","DOIUrl":"10.1007/s10469-023-09707-0","url":null,"abstract":"<div><div><p>A partial Hopf–Galois theory is developed for partial H-module algebras, and we recover analogs of classical results for Hopf algebras.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"385 - 406"},"PeriodicalIF":0.5,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50451043","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
Pre-Minimal Pairs and Homogeneous Valuations 预极小对与齐次估值
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-08-30 DOI: 10.1007/s10469-023-09705-2
Yu. L. Ershov
{"title":"Pre-Minimal Pairs and Homogeneous Valuations","authors":"Yu. L. Ershov","doi":"10.1007/s10469-023-09705-2","DOIUrl":"10.1007/s10469-023-09705-2","url":null,"abstract":"<div><div><p>We offer for consideration and study the concept of a pre-minimal pair. Also we examine extensions of valuations of a field <i>F</i> to valuations of the rational function field <i>F</i>(<i>x</i>) in one variable.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"363 - 371"},"PeriodicalIF":0.5,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50524839","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
Dynamic Temporal Logical Operations in Multi-Agent Logics 多Agent逻辑中的动态时态逻辑运算
IF 0.5 3区 数学
Algebra and Logic Pub Date : 2023-08-30 DOI: 10.1007/s10469-023-09708-z
V. V. Rybakov
{"title":"Dynamic Temporal Logical Operations in Multi-Agent Logics","authors":"V. V. Rybakov","doi":"10.1007/s10469-023-09708-z","DOIUrl":"10.1007/s10469-023-09708-z","url":null,"abstract":"<div><div><p>We study temporal multi-agent logics using a new approach to defining time for individual agents. It is assumed that in any time state each agent (in a sense) generates its own future time, which will only be available for analysis in the future. That is, the defined time interval depends both on the agent and on the initial state where the agent starts to act. It is also assumed that the agent may have intervals of forgotten (lost) time. We investigate problems of unification and problems of computable recognizing admissible inference rules. An algorithm is found for solving these problems based on the construction of a finite computable set of formulas which is a complete set of unifiers. We use the technique of projective formulas developed by S. Ghilardi. It is proved that any unifiable formula is in fact projective and an algorithm is constructed which creates its projective unifier. Thereby we solve the unification problem, and based at this, find the solution to the open problem of computable recognizing admissible inference rules.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 5","pages":"407 - 419"},"PeriodicalIF":0.5,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50524838","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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