International Journal of Algebra and Computation最新文献

{"title":"On the structure of finitely presented Bestvina–Brady groups","authors":"Priyavrat Deshpande, Mallika Roy","doi":"10.1142/s0218196724500012","DOIUrl":"https://doi.org/10.1142/s0218196724500012","url":null,"abstract":"<p>Right-angled Artin groups and their subgroups are of great interest because of their geometric, combinatorial and algorithmic properties. It is convenient to define these groups using finite simplicial graphs. The isomorphism type of the group is uniquely determined by the graph. Moreover, many structural properties of right-angled Artin groups can be expressed in terms of their defining graph.</p><p>In this paper, we address the question of understanding the structure of a class of subgroups of right-angled Artin groups in terms of the graph. Bestvina and Brady, in their seminal work, studied these subgroups (now called Bestvina–Brady groups or Artin kernels) from a finiteness conditions viewpoint. Unlike the right-angled Artin groups the isomorphism type of Bestvina–Brady groups is not uniquely determined by the defining graph. We prove that certain finitely presented Bestvina–Brady groups can be expressed as an iterated amalgamated product. Moreover, we show that this amalgamated product can be read off from the graph defining the ambient right-angled Artin group.</p>","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"2016 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140105993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchies","authors":"Jana Volaříková","doi":"10.1142/s0218196724500024","DOIUrl":"https://doi.org/10.1142/s0218196724500024","url":null,"abstract":"&lt;p&gt;We deal with the question of the &lt;span&gt;&lt;math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;-reducibility of pseudovarieties of ordered monoids corresponding to levels of concatenation hierarchies of regular languages. A pseudovariety of ordered monoids &lt;span&gt;&lt;math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mstyle mathvariant=\"sans-serif\"&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mstyle&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is called &lt;span&gt;&lt;math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;-reducible if, given a finite ordered monoid &lt;i&gt;M&lt;/i&gt;, for every inequality of pseudowords that is valid in &lt;span&gt;&lt;math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mstyle mathvariant=\"sans-serif\"&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mstyle&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, there exists an inequality of &lt;span&gt;&lt;math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;-words that is also valid in &lt;span&gt;&lt;math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mstyle mathvariant=\"sans-serif\"&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mstyle&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and has the same “imprint” in &lt;i&gt;M&lt;/i&gt;.&lt;/p&gt;&lt;p&gt;Place and Zeitoun have recently proven the decidability of the membership problem for levels &lt;span&gt;&lt;math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;∕&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, 1, &lt;span&gt;&lt;math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;∕&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and &lt;span&gt;&lt;math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;∕&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; of concatenation hierarchies with level 0 being a finite Boolean algebra of regular languages closed under quotients. The solutions of these membership problems have been found by considering a more general problem of separation of regular languages and its further generalization — a problem of covering. Following the results of Place and Zeitoun, we prove that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels &lt;span&gt;&lt;math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;∕&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and &lt;span&gt;&lt;math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;∕&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; are &lt;span&gt;&lt;math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;-reducible. As a corollary of these results, we obtain that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels &lt;span&gt;&lt;math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;∕&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"146 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140106337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Commuting and product-zero probability in finite rings","authors":"Pavel Shumyatsky, Matteo Vannacci","doi":"10.1142/s0218196724500061","DOIUrl":"https://doi.org/10.1142/s0218196724500061","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">cp</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>R</mi><mo stretchy=\"false\">)</mo></math></span><span></span> be the probability that two random elements of a finite ring <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>R</mi></math></span><span></span> commute and <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">zp</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>R</mi><mo stretchy=\"false\">)</mo></math></span><span></span> the probability that the product of two random elements in <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>R</mi></math></span><span></span> is zero. We show that if <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">cp</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>R</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mi>𝜀</mi></math></span><span></span>, then there exists a Lie-ideal <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi></math></span><span></span> in the Lie-ring <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>R</mi><mo>,</mo><mo stretchy=\"false\">[</mo><mo stretchy=\"false\">⋅</mo><mo>,</mo><mo stretchy=\"false\">⋅</mo><mo stretchy=\"false\">]</mo><mo stretchy=\"false\">)</mo></math></span><span></span> with <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝜀</mi></math></span><span></span>-bounded index and with <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">[</mo><mi>D</mi><mo>,</mo><mi>D</mi><mo stretchy=\"false\">]</mo></math></span><span></span> of <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝜀</mi></math></span><span></span>-bounded order. If <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">zp</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>R</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mi>𝜀</mi></math></span><span></span>, then there exists an ideal <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi></math></span><span></span> in <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mi>R</mi></math></span><span></span> with <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝜀</mi></math></span><span></span>-bounded index and <span><math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span> of <span><math altimg=\"eq-00016.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝜀</mi></math></span><span></span>-bounded order. These results are analogous to the well-known theorem of Neumann on the commuting probability in finite groups.</p>","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"29 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subpolygroup commutativity degree of finite extension polygroup","authors":"M. Al-Tahan, B. Davvaz, P. Harikrishnan, P. Pallavi","doi":"10.1142/s0218196723500698","DOIUrl":"https://doi.org/10.1142/s0218196723500698","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"253 7","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139011475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Detecting similarities of rational plane curves using complex differential invariants","authors":"H. A. Çoban","doi":"10.1142/s0218196723500686","DOIUrl":"https://doi.org/10.1142/s0218196723500686","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"130 ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139011530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Author index Volume 33 (2023)","authors":"","doi":"10.1142/s0218196723990011","DOIUrl":"https://doi.org/10.1142/s0218196723990011","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"21 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139194284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A census of small Schurian association schemes","authors":"Jesse Lansdown","doi":"10.1142/s0218196723500674","DOIUrl":"https://doi.org/10.1142/s0218196723500674","url":null,"abstract":"Using the classification of transitive groups of degree $n$, for $2 leqslant n leqslant 48$, we classify the Schurian association schemes of order $n$, and as a consequence, the transitive groups of degree $n$ that are $2$-closed. In addition, we compute the character table of each association scheme and provide a census of important properties. Finally, we compute the $2$-closure of each transitive group of degree $n$, for $2 leqslant n leqslant 48$. The results of this classification are made available as a supplementary database.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetric polynomials in free centre-by-metabelian lie algebras of rank 2","authors":"C. E. Kofinas","doi":"10.1142/s0218196723500662","DOIUrl":"https://doi.org/10.1142/s0218196723500662","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ℤ-Gradings on the Grassmann Algebra Over Infinite Fields: Graded Identities and Central Polynomials","authors":"Claudemir Fideles, Alan Guimaraes","doi":"10.1142/s0218196723500650","DOIUrl":"https://doi.org/10.1142/s0218196723500650","url":null,"abstract":"Let [Formula: see text] be the infinite-dimensional Grassmann algebra over an infinite field [Formula: see text] of characteristic different from 2. The main purpose of this paper is to describe the [Formula: see text]-ideal of the graded polynomial identities and the [Formula: see text]-space of the central polynomials of [Formula: see text] equipped with its [Formula: see text] and [Formula: see text]-induced [Formula: see text]-gradings. Therefore, we generalize the results of [A. Brandão, C. Fidelis and A. Guimarães, [Formula: see text]-gradings of full support on the Grassmann algebra, J. Algebra 601 (2022) 332–353; C. Fidelis, A. Guimarães and P. Koshlukov, A note on [Formula: see text]-gradings on the Grassmann algebra and elementary number theory, Linear Multilinear Algebra 71(7) (2023) 1244–1264] in the PI theory context.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" 85","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Separating Notions in Effective Topology","authors":"Alexander G. Melnikov, Keng Meng Ng","doi":"10.1142/s0218196723500649","DOIUrl":"https://doi.org/10.1142/s0218196723500649","url":null,"abstract":". We compare several natural notions of effective presentability of a topological space up to homeomorphism. We note that every left-c.e. (lower-semicomputable) Stone space is homeomorphic to a computable one. In contrast, we produce an example of a locally compact, left-c.e. space that is not homeomorphic to any computable Polish space. We apply a similar technique to produce examples of computable topological spaces not homeomorphic to any right-c.e. (upper-semicomputable) Polish space, and indeed to any arith-metical or even analytical Polish space. We then apply our techniques to totally disconnected locally compact (tdlc) groups. We prove that every effectively locally compact tdlc group is topologically isomorphic to a computable tdlc group; all notions will be clarified. The result is perhaps unexpected since the hypothesis of the theorem may seem rather weak.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136099404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}