Rough ideals based on ideal determined varieties
Saeed
Rasouli
Department of Mathematics, College of science, Persian Gulf University, Bushehr, 7516913817, Iran
author
text
article
2019
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
1
21
https://as.yazd.ac.ir/article_1334_1f96ca4bfe0b11bf90900393c834cde3.pdf
dx.doi.org/10.22034/as.2019.1334
Cartesian closed subcategories of topological fuzzes
Mahboobeh
Akbarpour
Department of Mathematics, University of Hormozgan, Bandarabbas, Iran
author
Ghasem
Mirhosseinkhani
Department of mathematics and Computer Sciences, Sirjan
University of Technology, Sirjan, Iran.
author
text
article
2019
eng
A category $\mathbf{C}$ is called Cartesian closed provided that it has finite products and for each$\mathbf{C}$-object $A$ the functor $(A\times -): A\ra A$ 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
23
33
https://as.yazd.ac.ir/article_1335_018fbb58821a70951c125fb1a128bb8d.pdf
dx.doi.org/10.22034/as.2019.1335
A general construction of Reed-Solomon codes based on generalized discrete Fourier transform
Najme
Sahami
Department of mathematical sciences, University of Kashan, Kashan, Isfahan, Iran.
author
Majid
Mazrooei
Department of mathematical sciences, University of Kashan, Kashan, Isfahan, Iran.
author
text
article
2019
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
35
45
https://as.yazd.ac.ir/article_1338_aaf2266a8d56cf0524ddd37ed9603a3f.pdf
dx.doi.org/10.22034/as.2019.1338
Graph product of generalized Cayley graphs over polygroups
Dariush
Heidari
Faculty of science,
Mahallat institute of higher education, Mahallat, Iran
author
Bijan
Davvaz
Department of Mathematics,
Yazd University, Yazd, Iran
author
text
article
2019
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
47
54
https://as.yazd.ac.ir/article_1340_88ceb8b077d43d4584c59fcdf85195c4.pdf
dx.doi.org/10.22034/as.2019.1340
Characterizing some groups with nilpotent derived subgroup
Azam
Kaheni
Department of Mathematics, University of Birjand, Birjand, Iran.
author
Farangis
Johari
Department of Pure Mathematics,
Ferdowsi University of Mashhad,
Mashhad, Iran.
author
text
article
2019
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
55
63
https://as.yazd.ac.ir/article_1353_9342431d85fe2fe2c85f3e6215bd75fe.pdf
dx.doi.org/10.22034/as.2019.1353
Constacyclic Codes of Arbitrary Length over $F_{q}+uF_{q}+\cdots +u^{e-1}F_{q}$
Marziyeh
Beygi
Department of Mathematics, College of Sciences, Shiraz University,
Shiraz, Iran
author
Shohreh
Namazi
Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran
author
Habib
Sharif
Department of Mathematics, College of Sciences, Shiraz University,
Shiraz, 71467-13565, Iran.
author
text
article
2019
eng
In this article, we shall study the structure of $(a+bu)-$constacyclic codes of arbitrary length over the ring$R=F_{q}+uF_{q}+\cdots +u^{e-1}F_{q}$, where $u^{e}=0$, $q$ is a power of a prime number $p$ and $a,b$ are non-zero elements of $F_{q}$. Also we shall find a minimal spanning set for these codes. %, and completely determine the structure of these codes. For a constacyclic code $C$ we shall determine its minimum Hamming distance with some properties of $Tor(C)$ as an $a-$constacyclic code over $F_{q}$.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
65
82
https://as.yazd.ac.ir/article_1355_8a201cea56ab8e4a73196e35893cbf91.pdf
dx.doi.org/10.22034/as.2019.1355
Isogeny-Based Certificateless Identification Scheme
Hassan
Daghigh
Department of mathematical science, University of Kashan, Kashan, Iran
author
Ruholla
Khodakaramian Gilan
Department of mathematical sciences, University of Kashan, Kashan, Iran.
author
text
article
2019
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
83
97
https://as.yazd.ac.ir/article_1357_aa4edd63853b166e72b369fbdf7a1dbd.pdf
dx.doi.org/10.22034/as.2019.1357
An elementary proof of Nagel-Schenzel formula
Alireza
Vahidi
Department of Mathematics, Payame Noor University (PNU), P.O.BOX, 19395-4697, Tehran, Iran
author
text
article
2019
eng
Let $R$ be a commutative Noetherian ring with non-zero identity, $\mathfrak{a}$ an ideal of $R$, $M$ a finitely generated $R$--module, and $a_1, \ldots, a_n$ an $\mathfrak{a}$--filter regular $M$--sequence. The formula\begin{align*}\operatorname{H}^i_\mathfrak{a}(M)\cong\left\{\begin{array}{lll}\operatorname{H}^i_{(a_1, \ldots, a_n)}(M) & \text{for all}\ \mathrm{i< n},\\\operatorname{H}^{i- n}_\mathfrak{a}(\operatorname{H}^n_{(a_1, \ldots, a_n)}(M)) & \text{for all}\ \mathrm{i\geq n},\end{array}\right.\end{align*}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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
99
102
https://as.yazd.ac.ir/article_1359_1eb2084645c2b5f9b62600efe0adf1ae.pdf
dx.doi.org/10.22034/as.2019.1359
Hyperrings which every element is sum of an idempotent and nilpotent
Yahya
Talebi
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
author
Marziyeh
Farzinejad
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
author
text
article
2019
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
103
114
https://as.yazd.ac.ir/article_1360_49631d4e52027e3f5b10ea79a408c66c.pdf
dx.doi.org/10.22034/as.2019.1360
A note on derivations in rings and Banach algebras
Nadeem
Rehman
Department of mathematics, Aligarh Muslim University, Aligarh, India.
author
Shuliang
Huang
School of Mathematics and Finance, Chuzhou University, Chuzhou, Anhui Province, P.R.China
author
Mohd
Raza
Department of Mathematics, Faculty of Science and Arts-Rabigh, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia.
author
text
article
2019
eng
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:$(i)$~ $d(x)\circ_n d(y)$=$x\circ _m y$ $(ii)$~$d(x)\circ_m d(y)$=$(d(x\circ y))^n$ 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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
115
125
https://as.yazd.ac.ir/article_1378_661a490ef5fc9de579717cacdf1c76ab.pdf
dx.doi.org/10.22034/as.2019.1378
An algebraic construction of QC-LDPC codes based on powers of primitive elements in a finite field and free of small ETSs
Farzane
Amirzade Dana
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
author
Meysam
Alishahi
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
author
Mohammad-Reza
Rafsanjani Sadeghi
Department of mathematics and computer Science, Amirkabir University of Technology, Tehran, Iran
author
text
article
2019
eng
An $(a,b)$ elementary trapping set (ETS), where $a$ and $b$ denote the size and the number of unsatisfied check nodes in the ETS, influences the performance of low-density parity-check (LDPC) codes. The smallest size of an ETS in LDPC codes with column weight 3 and girth 6 is 4. In this paper, we concentrate on a well-known algebraic-based construction of girth-6 QC-LDPC codes based on powers of a primitive element in a finite field $\mathbb{F}_q$. For this structure, we provide the sufficient conditions to obtain $3\times n$ submatrices of an exponent matrix in constructing girth-6 QC-LDPC codes whose ETSs have the size of at least 5. For structures on finite field $\mathbb{F}_q$, where $q$ is a power of 2, all non-isomorphic $3\times n$ submatrices of the exponent matrix which yield QC-LDPC codes free of small ETSs are presented.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
127
138
https://as.yazd.ac.ir/article_1394_2e4e15407cdb551558f9a7236494e374.pdf
dx.doi.org/10.22034/as.2019.1394
On the converse of Baer's theorem for generalizations of groups with trivial Frattini subgroups
Yasaman
Taghavi
Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran
author
Saeed
Kayvanfar
Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran
author
Marzieh
Chakaneh
Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran
author
text
article
2019
eng
In 2012, Guo and Gong proved that if $G$ is a finite nonabelian group with $\Phi(G)=1$, then $|G:Z(G)|<|G'||U(G)|$, in which $U(G)$ is the nilpotent residual of $G$. We show that the assumption of finiteness of the group can be omitted. Moreover, we investigate converse of Schur and Baer's theorems for groups that can be seen as generalizations of groups with trivial Frattini subgroups and state some properties of $n$-isoclinism families of these groups.
Algebraic Structures and Their Applications
Yazd University
2382-9761
6
v.
1
no.
2019
139
148
https://as.yazd.ac.ir/article_1396_9ec887c2f69ccc83a253fc6414df4ebe.pdf
dx.doi.org/10.22034/as.2019.1396