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Hojjat Mostafanasab

Publications and source records attributed to Hojjat Mostafanasab.

15 recordsLinked to original sources
arXiv2017

$b$-symbol distance distribution of repeated-root cyclic codes

Symbol-pair codes, introduced by Cassuto and Blaum [1], have been raised for symbol-pair read channels. This new idea is motivated by the limitation of the reading process in high-density data storage technologies. Yaakobi et al. [8] introduced codes for $b$-symbol read channels, where the read operation is performed as a consecutive sequence of $b>2$ symbols. In this paper, we come up with a method to compute the $b$-symbol-pair distance of two $n$-tuples, where $n$ is a positive integer. Also, we deal with the $b$-symbol-pair distances of some kind of cyclic codes of length $p^e$ over $\mathbb{F}_{p^m}$.

cs.IT↗
arXiv2016

Zero-Annihilator Graphs of Commutative Rings

Assume that $R$ is a commutative ring with nonzero identity. In this paper, we introduce and investigate zero-annihilator graph of $R$ denoted by $\mathtt{ZA}(R)$. It is the graph whose vertex set is the set of all nonzero nonunit elements of $R$ and two distinct vertices $x$ and $y$ are adjacent whenever ${\rm Ann}_R(x)\cap {\rm Ann}_R(y)=\{0\}$.

math.AC↗
arXiv2016

Weakly classical prime submodules

In this paper, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a classical prime submodule, if for each $m \in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$ or $bm\in N$. We introduce the concept of "weakly classical prime submodules." A proper submodule $N$ of $M$ is a weakly classical prime submodule if whenever $a,b\in R$ and $m\in M$ with $0\neq abm\in N$, then $am\in N$ or $bm\in N$.

math.AC↗
arXiv2016

On cyclic DNA codes over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$

In the present paper we study the structure of cyclic DNA codes of even lenght over the ring $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ where $u^3=0$. We investigate two presentations of cyclic codes of even lenght over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ satisfying the reverse constraint and reverse-complement constraint.

cs.IT↗
arXiv2016

On weakly $n$-absorbing ideals of commutative rings

All rings are commutative with $1\neq0$. The purpose of this paper is to investigate the concept of weakly $n$-absorbing ideals generalizing weakly 2-absorbing ideals. We prove that over a $u$-ring $R$ the Anderson-Badawi's conjectures about $n$-absorbing ideals and the Badawi-Yousefian's question about weakly 2-absorbing ideals hold.

math.AC↗
arXiv2015

Triple cyclic codes over $\mathbb{Z}_2$

Let $r,s,t$ be three positive integers and $\mathcal{C}$ be a binary linear code of lenght $r+s+t$. We say that $\mathcal{C}$ is a triple cyclic code of lenght $(r,s,t)$ over $\mathbb{Z}_2$ if the set of coordinates can be partitioned into three parts that any cyclic shift of the coordinates of the parts leaves invariant the code. These codes can be considered as $\mathbb{Z}_2[x]$-submodules of $\frac{\mathbb{Z}_2[x]}{\langle x^r-1\rangle}\times\frac{\mathbb{Z}_2[x]}{\langle x^s-1\rangle}\times\frac{\mathbb{Z}_2[x]}{\langle x^t-1\rangle}$. We give the minimal generating sets of this kind of codes. Also, we determine the relationship between the generators of triple cyclic codes and their duals.

cs.IT↗
arXiv2015

$ϕ$-classical prime submodules

In this paper, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a classical prime submodule, if for each $m\in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$ or $bm\in N$. Let $ϕ:S(M)\to S(M)\cup{\emptyset}$ be a function where $S(M)$ is the set of all submodules of $M$. We introduce the concept of "$ϕ$-classical prime submodules". A proper submodule $N$ of $M$ is a $ϕ$-classical prime submodule if whenever $a,b\in R$ and $m\in M$ with $abm\in N\backslashϕ(N)$, then $am\in N$ or $bm\in N$.

math.AC↗
arXiv2015

$(1-2u^2)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$

Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^2)$-constacyclic codes over the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$, where $u^3=u$. We describe generator polynomials of this kind of codes and investigate the structural properties of these codes by a decomposition theorem.

cs.IT↗
arXiv2015

Classical 2-absorbing submodules of modules over commutative rings

In this article, all rings are commutative with nonzero identity. Let $M$ be an $R$-module. A proper submodule $N$ of $M$ is called a classical prime submodule, if for each $m\in M$ and elements $a,b\in R$, $abm\in N$ implies that $am\in N$ or $bm\in N$. We introduce the concept of "classical 2-absorbing submodules" as a generalization of "classical prime submodules." We say that a proper submodule $N$ of $M$ is a classical 2-absorbing submodule if whenever $a,b,c\in R$ and $m\in M$ with $abcm\in N$, then $abm\in N$ or $acm\in N$ or $bcm\in N$.

math.AC↗
arXiv2015

Uniformly 2-absorbing primary ideals of commutative rings

In this study, we introduce the concept of "uniformly 2-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of 2-absorbing primary ideals of commutative rings. Then we investigate some properties of uniformly 2-absorbing primary ideals of commutative rings with examples. Also, we investigate a specific kind of uniformly 2-absorbing primary ideals by the name of "special 2-absorbing primary ideals".

math.AC↗
arXiv2015

On 2-absorbing primary submodules of modules over commutative rings

All rings are commutative with $1\neq0$, and all modules are unital. The purpose of this paper is to investigate the concept of $2$-absorbing primary submodules generalizing $2$-absorbing primary ideals of rings. Let $M$ be an $R$-module. A proper submodule $N$ of an $R$-module $M$ is called a $2$-absorbing primary submodule of $M$ if whenever $a,b\in R$ and $m\in M$ and $abm\in N$, then $am\in M$-$rad(N)$ or $bm\in M$-$rad(N)$ or $ab\in(N:_RM)$. It is shown that a proper submodule $N$ of $M$ is a $2$-absorbing primary submodule if and only if whenever $I_1I_2K\subseteq N$ for some ideals $I_1,I_2$ of $R$ and some submodule $K$ of $M$, then $I_1I_2\subseteq(N:_RM)$ or $I_1K\subseteq M$-$rad(N)$ or $I_2K\subseteq M$-$rad(N)$. We prove that for a submodule $N$ of an $R$-module $M$ if $M$-$rad(N)$ is a prime submodule of $M$, then $N$ is a $2$-absorbing primary submodule of $M$. If $N$ is a $2$-absorbing primary submodule of a finitely generated multiplication $R$-module $M$, then $(N:_RM)$ is a $2$-absorbing primary ideal of $R$ and $M$-$rad(N)$ is a $2$-absorbing submodule of $M$.

math.AC↗
arXiv2015

On endo-prime and endo-coprime modules

The aim of this paper is to investigate properties of endo-prime and endo-coprime modules which are generalizations of prime and simple rings, respectively. Various properties of endo-coprime modules are obtained. Duality-like connections are established for endo-prime and endo-coprime modules.

math.RA↗
arXiv2015

On ϕ-n-absorbing primary ideals of commutative rings

All rings are commutative with $1$ and $n$ is a positive integer. Let $ϕ: J(R)\to J(R)\cup{\emptyset}$ be a function where $J(R)$ denotes the set of all ideals of $R$. We say that a proper ideal $I$ of $R$ is $ϕ$-$n$-absorbing primary if whenever $a_1,a_2,...,a_{n+1}\in R$ and $a_1a_2\cdots a_{n+1}\in I\backslashϕ(I)$, either $a_1a_2\cdots a_n\in I$ or the product of $a_{n+1}$ with $(n-1)$ of $a_1,...,a_n$ is in $\sqrt{I}$. The aim of this paper is to investigate the concept of $ϕ$-$n$-absorbing primary ideals.

math.AC↗
arXiv2015

2-irreducible and strongly 2-irreducible ideals of commutative rings

An ideal I of a commutative ring R is said to be irreducible if it cannot be written as the intersection of two larger ideals. A proper ideal I of a ring R is said to be strongly irreducible if for each ideals J, K of R, J\cap K\subseteq I implies that J\subset I or K\subset I. In this paper, we introduce the concepts of 2-irreducible and strongly 2-irreducible ideals which are generalizations of irreducible and strongly irreducible ideals, respectively. We say that a proper ideal I of a ring R is 2-irreducible if for each ideals J, K and L of R, I= J\cap K\cap L implies that either I=J\cap K or I=J\cap L or I=K\cap L. A proper ideal I of a ring R is called strongly 2-irreducible if for each ideals J, K and L of R, J\cap K\cap L\subseteq I implies that either J\cap K\subseteq I or J\cap L\subseteq I or K\cap L\subseteq I.

math.AC↗