{"title":"Constacyclic Codes of Arbitrary Length over Fq+uFq+⋯+ue−1Fq","authors":"M. Beygi, S. Namazi, H. Sharif","doi":"10.29252/ASTA.6.1.67","DOIUrl":"https://doi.org/10.29252/ASTA.6.1.67","url":null,"abstract":"","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76784251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let R be a prime ring with U the Utumi quotient ring and Q be the Martindale quotient ring of R, respectively. Let d be a derivation of R and m,n be fixed positive integers. In this paper, we study the case when one of the following holds: (i) d(x) ◦n d(y)=x ◦m y (ii) d(x) ◦m d(y)=(d(x ◦ y)) for all x, y in some appropriate subset of R. We also examine the case where R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on Banach algebras.
设R为素环，U为Utumi商环，Q为R的Martindale商环。设d是R和m的导数，n是固定的正整数。在本文中，我们研究了下列条件之一成立的情况:(i) d(x) * n d(y)=x * m y (ii) d(x) * m d(y)=(d(x * y)))对于R的某些适当子集中的所有x, y，我们还研究了R是半素环的情况。最后，作为一个应用，我们将我们的结果应用于Banach代数上的连续导数。
{"title":"A note on derivations in rings and Banach algebras","authors":"N. Rehman, Shuliang Huang, M. Raza","doi":"10.29252/as.2019.1378","DOIUrl":"https://doi.org/10.29252/as.2019.1378","url":null,"abstract":"Let R be a prime ring with U the Utumi quotient ring and Q be the Martindale quotient ring of R, respectively. Let d be a derivation of R and m,n be fixed positive integers. In this paper, we study the case when one of the following holds: (i) d(x) ◦n d(y)=x ◦m y (ii) d(x) ◦m d(y)=(d(x ◦ y)) for all x, y in some appropriate subset of R. We also examine the case where R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on Banach algebras.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84314197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, groups with trivial intersection between Frattini and derived subgroups are considered. First, some structural properties of these groups are given in an important special case. Then, some family invariants of each n-isoclinism family of such groups are stated. In particular, an explicit bound for the order of each center factor group in terms of the order of its derived subgroup is also provided.
{"title":"Characterizing some groups with nilpotent derived subgroup","authors":"A. Kaheni, F. Johari","doi":"10.29252/as.2019.1353","DOIUrl":"https://doi.org/10.29252/as.2019.1353","url":null,"abstract":"In this paper, groups with trivial intersection between Frattini and derived subgroups are considered. First, some structural properties of these groups are given in an important special case. Then, some family invariants of each n-isoclinism family of such groups are stated. In particular, an explicit bound for the order of each center factor group in terms of the order of its derived subgroup is also provided.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88557824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes enjoy nice algebraic properties just as the classic one.
{"title":"A general construction of Reed-Solomon codes based on generalized discrete Fourier transform","authors":"N. Sahami, M. Mazrooei","doi":"10.29252/AS.2019.1338","DOIUrl":"https://doi.org/10.29252/AS.2019.1338","url":null,"abstract":"In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes enjoy nice algebraic properties just as the classic one.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80997316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A category $mathbf{C}$ is called Cartesian closed provided that it has finite products and for each$mathbf{C}$-object $A$ the functor $(Atimes -): Ara A$ has a right adjoint. It is well known that the category $mathbf{TopFuzz}$ of all topological fuzzes is both complete and cocomplete, but it is not Cartesian closed. In this paper, we introduce some Cartesian closed subcategories of this category.
{"title":"Cartesian closed subcategories of topological fuzzes","authors":"M. Akbarpour, Ghasem Mirhosseinkhani","doi":"10.29252/AS.2019.1335","DOIUrl":"https://doi.org/10.29252/AS.2019.1335","url":null,"abstract":"A category $mathbf{C}$ is called Cartesian closed provided that it has finite products and for each$mathbf{C}$-object $A$ the functor $(Atimes -): Ara A$ has a right adjoint. It is well known that the category $mathbf{TopFuzz}$ of all topological fuzzes is both complete and cocomplete, but it is not Cartesian closed. In this paper, we introduce some Cartesian closed subcategories of this category.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75846603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a finitely generated R–module, and a1, . . . , an an a–filter regular M–sequence. The formula Ha(M) ∼= H i (a1,...,an) (M) for all i < n, Hi−n a (H n (a1,...,an) (M)) for all i ≥ n, is known as Nagel-Schenzel formula and is a useful result to express the local cohomology modules in terms of filter regular sequences. In this paper, we provide an elementary proof to this formula.
设R是一个非零单位元的交换诺瑟环，a是R的理想，M是一个有限生成的R模，a1，…，一个a -滤波器正则m序列。公式Ha(M) ~ =Hi (a1，…，an) (M)对于所有i < n, Hi - n a(H n (a1，…，an) (M))对于所有i≥n，被称为Nagel-Schenzel公式，它是用滤波正则序列表示局部上同模的一个有用的结果。本文给出了这个公式的初等证明。
{"title":"An elementary proof of Nagel-Schenzel formula","authors":"A. Vahidi","doi":"10.29252/AS.2019.1359","DOIUrl":"https://doi.org/10.29252/AS.2019.1359","url":null,"abstract":"Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a finitely generated R–module, and a1, . . . , an an a–filter regular M–sequence. The formula Ha(M) ∼= H i (a1,...,an) (M) for all i < n, Hi−n a (H n (a1,...,an) (M)) for all i ≥ n, is known as Nagel-Schenzel formula and is a useful result to express the local cohomology modules in terms of filter regular sequences. In this paper, we provide an elementary proof to this formula.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"94 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72375129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ideals in an algebraic structure, are introduced and investigated.
{"title":"Rough ideals based on ideal determined varieties","authors":"S. Rasouli","doi":"10.29252/AS.2019.1334","DOIUrl":"https://doi.org/10.29252/AS.2019.1334","url":null,"abstract":"The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ideals in an algebraic structure, are introduced and investigated.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77274897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we propose a new certificateless identification scheme based on isogenies between elliptic curves that is a candidate for quantum-resistant problems. The proposed scheme has the batch verification property which allows verifying more than one identity by executing only a single challenge-response protocol.
{"title":"Isogeny-Based Certificateless Identification Scheme","authors":"H. Daghigh, R. K. Gilan","doi":"10.29252/as.2019.1357","DOIUrl":"https://doi.org/10.29252/as.2019.1357","url":null,"abstract":"In this paper, we propose a new certificateless identification scheme based on isogenies between elliptic curves that is a candidate for quantum-resistant problems. The proposed scheme has the batch verification property which allows verifying more than one identity by executing only a single challenge-response protocol.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91127107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we define a generalized of clean of Krasner hyperrings for general hyperrings based on the notation of nilpotent elements of a general hyperring R, named nil clean hyperring. We examine characterization of this kind of hyperrings and finally, we obtain some relations of nil clean general hyperrings with other hyperrings.
本文基于一般超环R的幂零元符号，定义了一般超环的广义clean - of - Krasner超环，命名为nil clean -超环。研究了这类超环的性质，最后得到了零干净一般超环与其他超环的一些关系。
{"title":"Hyperrings which every element is sum of an idempotent and nilpotent","authors":"Y. Talebi, M. Farzinejad","doi":"10.29252/AS.2019.1360","DOIUrl":"https://doi.org/10.29252/AS.2019.1360","url":null,"abstract":"In this paper, we define a generalized of clean of Krasner hyperrings for general hyperrings based on the notation of nilpotent elements of a general hyperring R, named nil clean hyperring. We examine characterization of this kind of hyperrings and finally, we obtain some relations of nil clean general hyperrings with other hyperrings.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78368583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce a suitable generalization of Cayley graphs that is defined over polygroups (GCP-graph) and give some examples and properties. Then, we mention a generalization of NEPS that contains some known graph operations and apply to GCP-graphs. Finally, we prove that the product of GCP-graphs is again a GCP-graph.
{"title":"Graph product of generalized Cayley graphs over polygroups","authors":"D. Heidari","doi":"10.29252/AS.2019.1340","DOIUrl":"https://doi.org/10.29252/AS.2019.1340","url":null,"abstract":"In this paper, we introduce a suitable generalization of Cayley graphs that is defined over polygroups (GCP-graph) and give some examples and properties. Then, we mention a generalization of NEPS that contains some known graph operations and apply to GCP-graphs. Finally, we prove that the product of GCP-graphs is again a GCP-graph.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84857498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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