Pub Date : 2023-10-27DOI: 10.1142/s0219498825500665
Christopher Battarbee, Delaram Kahrobaei, Siamak F. Shahandashti
Of the many families of cryptographic schemes proposed to be post-quantum, a relatively unexplored set of examples comes from group-based cryptography. One of the more central schemes from this area is the so-called Semidirect Product Key Exchange (SDPKE), a generalization of Diffie–Hellman Key Exchange that is plausibly post-quantum. In this report we survey the state of the literature relating to SDPKE, providing a high-level discussion of security, as well as a comprehensive overview of the proposed platforms and the main cryptanalytic ideas relevant to each.
{"title":"Semidirect Product Key Exchange: the State of Play","authors":"Christopher Battarbee, Delaram Kahrobaei, Siamak F. Shahandashti","doi":"10.1142/s0219498825500665","DOIUrl":"https://doi.org/10.1142/s0219498825500665","url":null,"abstract":"Of the many families of cryptographic schemes proposed to be post-quantum, a relatively unexplored set of examples comes from group-based cryptography. One of the more central schemes from this area is the so-called Semidirect Product Key Exchange (SDPKE), a generalization of Diffie–Hellman Key Exchange that is plausibly post-quantum. In this report we survey the state of the literature relating to SDPKE, providing a high-level discussion of security, as well as a comprehensive overview of the proposed platforms and the main cryptanalytic ideas relevant to each.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"22 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136233164","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}
Pub Date : 2023-10-27DOI: 10.1142/s0219498825501208
Lei Sun
{"title":"Abundance and magnifying elements in transformation semigroups that preserve order and equivalence","authors":"Lei Sun","doi":"10.1142/s0219498825501208","DOIUrl":"https://doi.org/10.1142/s0219498825501208","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"148 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312462","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}
Pub Date : 2023-10-27DOI: 10.1142/s0219498825501221
A. L. Garcia-Pulido, G. Salgado
In this article we investigate the question of the lowest possible dimension that a sympathetic Lie algebra $mathfrak{g}$ can attain, when its Levi subalgebra $mathfrak{g}_L$ is simple. We establish the structure of the nilradical of a perfect Lie algebra $mathfrak{g}$, as a $mathfrak{g}_L$-module, and determine the possible Lie algebra structures that one such $mathfrak{g}$ admits. We prove that, as a $mathfrak{g}_L$-module, the nilradical must decompose into at least 4 simple modules. We explicitly calculate the semisimple derivations of a perfect Lie algebra $mathfrak{g}$ with Levi subalgebra $mathfrak{g}_L = mathfrak{sl}_2(mathbb{C})$ and give necessary conditions for $mathfrak{g}$ to be a sympathetic Lie algebra in terms of these semisimple derivations. We show that there is no sympathetic Lie algebra of dimension lower than 15, independently of the nilradical's decomposition. If the nilradical has 4 simple modules, we show that a sympathetic Lie algebra has dimension greater or equal than 25.
{"title":"On the existence of sympathetic lie algebras with dimension less than 25","authors":"A. L. Garcia-Pulido, G. Salgado","doi":"10.1142/s0219498825501221","DOIUrl":"https://doi.org/10.1142/s0219498825501221","url":null,"abstract":"In this article we investigate the question of the lowest possible dimension that a sympathetic Lie algebra $mathfrak{g}$ can attain, when its Levi subalgebra $mathfrak{g}_L$ is simple. We establish the structure of the nilradical of a perfect Lie algebra $mathfrak{g}$, as a $mathfrak{g}_L$-module, and determine the possible Lie algebra structures that one such $mathfrak{g}$ admits. We prove that, as a $mathfrak{g}_L$-module, the nilradical must decompose into at least 4 simple modules. We explicitly calculate the semisimple derivations of a perfect Lie algebra $mathfrak{g}$ with Levi subalgebra $mathfrak{g}_L = mathfrak{sl}_2(mathbb{C})$ and give necessary conditions for $mathfrak{g}$ to be a sympathetic Lie algebra in terms of these semisimple derivations. We show that there is no sympathetic Lie algebra of dimension lower than 15, independently of the nilradical's decomposition. If the nilradical has 4 simple modules, we show that a sympathetic Lie algebra has dimension greater or equal than 25.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"18 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312437","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}
Pub Date : 2023-10-27DOI: 10.1142/s0219498825501233
Emzar Khmaladze, Manuel Ladra
{"title":"<i>q</i>-crossed modules and <i>q</i>-capability of Lie algebras","authors":"Emzar Khmaladze, Manuel Ladra","doi":"10.1142/s0219498825501233","DOIUrl":"https://doi.org/10.1142/s0219498825501233","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"15 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312496","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}
Pub Date : 2023-10-20DOI: 10.1142/s0219498825500860
F. Ranjbar Hamghavandi, M. Ebrahimpour
Let [Formula: see text] be a positive integer. In this paper, we introduce a functional method, which gives us an equivalent condition to the concept of [Formula: see text]-absorbing primary submodules. By using this method, the dual notion of [Formula: see text]-absorbing primary submodules, which we call [Formula: see text]-secondary submodules, is presented. Then, some properties of this class of submodules, several useful examples and functorial results are presented.
{"title":"Some Remarks on the Dual Notion of <i>n</i>-Absorbing Primary Submodules","authors":"F. Ranjbar Hamghavandi, M. Ebrahimpour","doi":"10.1142/s0219498825500860","DOIUrl":"https://doi.org/10.1142/s0219498825500860","url":null,"abstract":"Let [Formula: see text] be a positive integer. In this paper, we introduce a functional method, which gives us an equivalent condition to the concept of [Formula: see text]-absorbing primary submodules. By using this method, the dual notion of [Formula: see text]-absorbing primary submodules, which we call [Formula: see text]-secondary submodules, is presented. Then, some properties of this class of submodules, several useful examples and functorial results are presented.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514299","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}
Pub Date : 2023-10-20DOI: 10.1142/s0219498825500835
Iulia Catalina Plesca, Marius Tarnauceanu
In this paper, we introduce a new function computing the harmonic mean of element orders of a finite group. We present a series of properties for this function, and then we study groups for which the value of the function is an integer.
{"title":"Finite groups with integer harmonic mean of element orders","authors":"Iulia Catalina Plesca, Marius Tarnauceanu","doi":"10.1142/s0219498825500835","DOIUrl":"https://doi.org/10.1142/s0219498825500835","url":null,"abstract":"In this paper, we introduce a new function computing the harmonic mean of element orders of a finite group. We present a series of properties for this function, and then we study groups for which the value of the function is an integer.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"15 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514304","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}
Pub Date : 2023-10-20DOI: 10.1142/s0219498825501142
Nan Gao, Keyan Song, Hanyang You, Guodong Zhou
{"title":"Resolving subcategories and singularity categories","authors":"Nan Gao, Keyan Song, Hanyang You, Guodong Zhou","doi":"10.1142/s0219498825501142","DOIUrl":"https://doi.org/10.1142/s0219498825501142","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566616","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}
Pub Date : 2023-10-20DOI: 10.1142/s0219498825500823
Gahininath Sonawane, Ganesh S. Kadu, Y. M. Borse
Let [Formula: see text] be a finite reduced ring with [Formula: see text] maximal ideals [Formula: see text] and let [Formula: see text] be the zero-divisor graph associated to [Formula: see text] The class of rings [Formula: see text] contains the Boolean rings as a subclass. When [Formula: see text] for all [Formula: see text] where [Formula: see text] is a finite field, we associate two [Formula: see text] sized matrices [Formula: see text] and [Formula: see text] to the graph [Formula: see text] having combinatorial entries and use these matrices to determine the spectrum of this graph. More precisely, we show that every eigenvalue of [Formula: see text] and of [Formula: see text] is an eigenvalue of [Formula: see text] To do this, we give a recursive description of the adjacency matrix of this graph and also exhibit its equitable partition. This is used in computing the determinant, rank and nullity of the adjacency matrix. Further, we propose that the eigenvalues of [Formula: see text] [Formula: see text] and the eigenvalue [Formula: see text] exhaust all the eigenvalues of [Formula: see text]
{"title":"Spectra of Zero-Divisor Graphs of Finite Reduced Rings","authors":"Gahininath Sonawane, Ganesh S. Kadu, Y. M. Borse","doi":"10.1142/s0219498825500823","DOIUrl":"https://doi.org/10.1142/s0219498825500823","url":null,"abstract":"Let [Formula: see text] be a finite reduced ring with [Formula: see text] maximal ideals [Formula: see text] and let [Formula: see text] be the zero-divisor graph associated to [Formula: see text] The class of rings [Formula: see text] contains the Boolean rings as a subclass. When [Formula: see text] for all [Formula: see text] where [Formula: see text] is a finite field, we associate two [Formula: see text] sized matrices [Formula: see text] and [Formula: see text] to the graph [Formula: see text] having combinatorial entries and use these matrices to determine the spectrum of this graph. More precisely, we show that every eigenvalue of [Formula: see text] and of [Formula: see text] is an eigenvalue of [Formula: see text] To do this, we give a recursive description of the adjacency matrix of this graph and also exhibit its equitable partition. This is used in computing the determinant, rank and nullity of the adjacency matrix. Further, we propose that the eigenvalues of [Formula: see text] [Formula: see text] and the eigenvalue [Formula: see text] exhaust all the eigenvalues of [Formula: see text]","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514301","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}
Pub Date : 2023-10-20DOI: 10.1142/s0219498825501178
Blake Norman
{"title":"Sharp Permutation Groups Whose Point Stabilizers are AGL(1,<i>p</i>)","authors":"Blake Norman","doi":"10.1142/s0219498825501178","DOIUrl":"https://doi.org/10.1142/s0219498825501178","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"3 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566620","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}
Pub Date : 2023-10-20DOI: 10.1142/s0219498825501191
Dejun Wu, Hui Zhou, Yongduo Wang
{"title":"Gorenstein AC-Projective and AC-Injective Representations of Quivers","authors":"Dejun Wu, Hui Zhou, Yongduo Wang","doi":"10.1142/s0219498825501191","DOIUrl":"https://doi.org/10.1142/s0219498825501191","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566619","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}
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