Papers by Ahmad Yousefian Darani
Digital Signal Processing
arXiv: Commutative Algebra, Feb 28, 2015
All rings are commutative with 1 = 0 and n is a positive integer. Let φ : J(R) → J(R)∪{∅} be a fu... more All rings are commutative with 1 = 0 and n is a positive integer. Let φ : J(R) → J(R)∪{∅} 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 ∈ R and a 1 a 2 • • • a n+1 ∈ I\φ(I), either a 1 a 2 • • • an ∈ I or the product of a n+1 with (n − 1) of a 1 ,. .. , an is in √ I. The aim of this paper is to investigate the concept of φ-n-absorbing primary ideals.
Advances in Mathematics of Communications, 2022
Traditional regenerating codes are efficient tools to optimize both storage and repair bandwidth ... more Traditional regenerating codes are efficient tools to optimize both storage and repair bandwidth in storing data across a distributed storage system, particularly in comparison to erasure codes and data replication. In traditional regenerating codes, the collection of any \begin{document}$ k $\end{document} nodes can reconstruct all stored information and is called the reconstruction set, \begin{document}$ \aleph _R $\end{document}. A failed node can be regenerated from any \begin{document}$ d $\end{document} surviving nodes. These collections of \begin{document}$ d $\end{document} nodes are called the regeneration sets, \begin{document}$ \aleph _H $\end{document}. The number of reconstruction sets and the number of regeneration sets satisfy \begin{document}$ |\aleph _R| = C_n^k $\end{document} and \begin{document}$ |\aleph _H| = C_{n-1}^d $\end{document}. In generalized regenerating codes, we will have, \begin{document}$ 1\le|\aleph_R|\le C^k_n $\end{document} and \begin{document}$...
Let M be a module over the commutative ring R. In this paper we introduce two new notions, namely... more Let M be a module over the commutative ring R. In this paper we introduce two new notions, namely strongly coprimal and super coprimal modules. Denote by ZR(M) the set of all zero-divisors of R on M. M is said to be strongly coprimal (resp. super coprimal) if for arbitrary a, b ∈ ZR(M) (resp. every finite subset F of ZR(M)) the annihilator of {a, b} (resp. F) in M is non-zero. In this paper we give some results on these classes of modules. Also we provide a relationship between the families of coprimal, strongly coprimal and super coprimal modules. We prove that if M is a coprimal module of finite Goldie dimension over a commutative ring, then M is super coprimal. Finally we show that every proper submodule of a module over a Prüfer domain of finite character can be expressed as a finite intersection of strongly primal submodules. 1
Abstract. Let R be a commutative ring with identity. Let ϕ: I(R) → I(R) ∪ {∅} be a function where... more Abstract. Let R be a commutative ring with identity. Let ϕ: I(R) → I(R) ∪ {∅} be a function where I(R) denotes the set of all ideals of R. A proper ideal Q of R is called ϕ-primary if whenever a, b ∈ R, ab ∈ Q−ϕ(Q) implies that either a ∈ Q or b ∈ √ Q. So if we take ϕ∅(Q) = ∅ (resp., ϕ0(Q) = 0), a ϕ-primary ideal is primary (resp., weakly primary). In this paper we study the properties of several generalizations of primary ideals of R. AMS Mathematics Subject Classification (2010): 13A15 Key words and phrases: primary ideal, weakly primary ideal, almost primary ideal, ϕ-primary ideal, strongly primary ideal 1.
Let M be a module over the commutative ring R. In this paper we introduce two new notions, namely... more Let M be a module over the commutative ring R. In this paper we introduce two new notions, namely strongly coprimal and super coprimal modules. Denote by ZR(M) the set of all zero-divisors of R on M . M is said to be strongly coprimal (resp. super coprimal) if for arbitrary a, b ∈ ZR(M) (resp. every finite subset F of ZR(M)) the annihilator of {a, b} (resp. F ) in M is non-zero. In this paper we give some results on these classes of modules. Also we provide a relationship between the families of coprimal, strongly coprimal and super coprimal modules. We prove that if M is a coprimal module of finite Goldie dimension over a commutative ring, then M is super coprimal. Finally we show that every proper submodule of a module over a Prüfer domain of finite character can be expressed as a finite intersection of strongly primal submodules.
ArXiv, 2016
In the present paper we study the structure of cyclic DNA codes of even lenght over the ring $\ma... more 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.
The purpose of this paper is to introduce some new classes of modules which is closely related to... more The purpose of this paper is to introduce some new classes of modules which is closely related to the classes of sharp modules, pseudo-Dedekind modules and \(TV\)-modules. In this paper we introduce the concepts of \(\Phi\)-sharp modules, \(\Phi\)-pseudo-Dedekind modules and \(\Phi\)-\(TV\)-modules. Let \(R\) be a commutative ring with identity and set \(\mathbb{H}=\lbrace M\mid M\) is an \(R\)-module and \(\operatorname{Nil}(M)\) is a divided prime submodule of \(M\rbrace\). For an \(R\)-module \(M\in\mathbb{H}\), set \(T=(R\setminus Z(M))\cap (R\setminus Z(R))\), \(\mathfrak{T}(M)=T^{-1}(M)\) and \(P:=(\operatorname{Nil}(M):_{R}M)\). In this case the mapping \(\Phi:\mathfrak{T}(M)\longrightarrow M_{P}\) given by \(\Phi(x/s)=x/s\) is an \(R\)-module homomorphism. The restriction of \(\Phi\) to \(M\) is also an \(R\)-module homomorphism from \(M\) in to \(M_{P}\) given by \(\Phi(m/1)=m/1\) for every \(m\in M\). An \(R\)-module \(M\in \mathbb{H}\) is called a \(\Phi\)-sharp module if...
This article introduces the notions quasi-co-\(n\)-absorbing preradicals and semi-co-\(n\)-absorb... more This article introduces the notions quasi-co-\(n\)-absorbing preradicals and semi-co-\(n\)-absorbing preradicals, generalizing the concept of semicoprime preradicals. We study the concepts quasi-co-\(n\)-absorbing submodules and semi-co-\(n\)-absorbing submodules and their relations with quasi-co-\(n\)-absorbing preradicals and semi-co-\(n\)-absorbing preradicals using the lattice structure of preradicals.
All rings are commutative with 1 6= 0. The purpose of this paper is to investigate the concept of... more All rings are commutative with 1 6= 0. 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.
Thai Journal of Mathematics, 2017
Let R be a commutative ring and n be a positive integer. A proper ideal I of R is called an n-abs... more Let R be a commutative ring and n be a positive integer. A proper ideal I of R is called an n-absorbing ideal if whenever x_1...x_{n+1}\in I for x_1,...,x_{n+1}\in R, then there are n of the x_i's whose product is in I. We give a generalization of Prime Avoidance Theorem. Also, an n-Absorbing Avoidance Theorem is proved. Moreover, we introduce the notions of quasi-n-absorbing ideals and of semi-n-absorbing ideals. We say that a proper ideal I of R is a quasi-n-absorbing ideal if whenever a^nb\in I for a,b\in R, then a^n\in I or a^{n-1}b\in I. A proper ideal I of R is said to be a semi-n-absorbing ideal if whenever a^{n+1}\in I for a\in R, then a^n\in I.
We introduce reduced modules over a commutative ring and z-submodules. Let R be a commutative rin... more We introduce reduced modules over a commutative ring and z-submodules. Let R be a commutative ring andM an R-module. An R-module M is called reduced if M has no nonzero nilpotent elements. A proper submodule N of M is called a z-submodule if for each m ∈ N , the intersection of all minimal prime submodules of M containing m is contained inN . We denote by h(S), for S ⊆ M , the set of all minimal prime submodules of M containing S. IfM is a faithful multiplication reducedR-module, then a prime submodule N of M is minimal if and only if for any m ∈ N there exists r ∈ R \ (N :R M) such that rm = 0. Also, for S ⊆ M , annR(S)M = ∩ Q, where Q ∈ Min(M) \ h(S). Moreover, if N is a nilpotent z-submodule of M , then every prime submodule of M , minimal over N is a prime z-submodule and N is equal to an intersection of prime z-submodules. We introduce property A onM and show that, if the R-moduleM satisfies property A, then any submodule N ofM is contained in a z-submodule.
Journal of Algebra and Its Applications
Let [Formula: see text] be a commutative ring, [Formula: see text] be an ideal of [Formula: see t... more Let [Formula: see text] be a commutative ring, [Formula: see text] be an ideal of [Formula: see text], [Formula: see text] be a non-null positive integer and [Formula: see text] be a function where [Formula: see text] is the set of ideals of [Formula: see text]. In this paper, we define a new generalization of strongly [Formula: see text]-irreducible ideals called strongly [Formula: see text]-[Formula: see text]-irreducible ideal, that is, whenever [Formula: see text] and [Formula: see text] for [Formula: see text] ideals of [Formula: see text], then there are [Formula: see text] of the [Formula: see text]’s whose intersection is in [Formula: see text]. We study the stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal.
Georgian Mathematical Journal
In this paper, we introduce some classes of R-modules that are closely related to the classes of ... more In this paper, we introduce some classes of R-modules that are closely related to the classes of Prüfer, Dedekind and Bezout modules. Let R be a commutative ring with identity and set \mathbb{H}=\bigl{\{}M\mid M\text{ is an }R\text{-module and }\mathrm{Nil}(M)% \text{ is a divided prime submodule of }M\bigr{\}}. For an R-module {M\in\mathbb{H}} , set {T=(R\setminus Z(R))\cap(R\setminus Z(M))} , {\mathfrak{T}(M)=T^{-1}M} and {P=(\mathrm{Nil}(M):_{R}M)} . In this case, the mapping {\Phi:\mathfrak{T}(M)\to M_{P}} given by {\Phi(x/s)=x/s} is an R-module homomorphism. The restriction of Φ to M is also an R-module homomorphism from M into {M_{P}} given by {\Phi(x)=x/1} for every {x\in M} . A nonnil submodule N of M is said to be Φ-invertible if {\Phi(N)} is an invertible submodule of {\Phi(M)} . Moreover, M is called a Φ-Prüfer module if every finitely generated nonnil submodule of M is Φ-invertible. If every nonnil submodule of M is Φ-invertible, then we say that M is a Φ-Dedekind module...
Communications in Mathematics and Statistics
Hacettepe Journal of Mathematics and Statistics
Tamkang Journal of Mathematics
Let $R$ be a commutative ring and let $M$ be an $R$-module. A submodule $N$ of $M$ is called a we... more Let $R$ be a commutative ring and let $M$ be an $R$-module. A submodule $N$ of $M$ is called a weakly primal submodule provided that the set $ P = w(N) \cup \{ 0 \} $ forms an ideal of $R$. Here $w(N)$ is the set of elements of $R$ that are not weakly prime to $N$, where an element $ r \in R $ is not weakly prime to $N$ if $ 0 \neq rm \in N $ for some $ m \in M \backslash N $. In this paper we give some basic results about weakly primal submodules. Also we discuss on the relations between the classes of the weakly primal submodules of $M$ and the weakly primal submodules of modules of fractions of $M$.
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Papers by Ahmad Yousefian Darani