Papers by esmaeil rostami
In this article, the concept of pseudo-irreducible ideals in a residuated lattice is introduced a... more In this article, the concept of pseudo-irreducible ideals in a residuated lattice is introduced and we consider its relationship with some important concepts of residuated lattices such as prime ideal and maximal ideal. Then using this concept, we define and study complete comaximal decomposition in residuated lattices. In particular, we characterize residuated lattices whose proper ideals can be written as an intersection of pairwise comaximal of finitely many pseudo-irreducible ideals.
Comaximal factorization of lifting ideals
Journal of Algebra and Its Applications, 2020
A proper ideal [Formula: see text] of a commutative ring [Formula: see text] is called lifting wh... more A proper ideal [Formula: see text] of a commutative ring [Formula: see text] is called lifting whenever idempotents of [Formula: see text] lift to idempotents of [Formula: see text]. In this paper, many of the basic properties of lifting ideals are studied and we prove and extend some well-known results concerning lifting ideals and lifting idempotents by a new approach. Furthermore, we give a necessary and sufficient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal lifting ideals.
Iranian Journal of Mathematical Sciences and Informatics, 2019
In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-... more In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free R-submodules of a finite quasi-Frobenius ring R which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Gröbner basis and we show that under certain conditions a linear code takes the maximum of minimum Hamming weight.
Bulletin of The Iranian Mathematical Society, 2015
In this paper we focus on a special class of commutative lo- cal rings called SPAP-rings and stud... more In this paper we focus on a special class of commutative lo- cal rings called SPAP-rings and study the relationship between this class and other classes of rings. We characterize the structure of modules and especially, the prime submodules of free modules over an SPAP-ring and derive some basic properties. Then we answer the question of Lam and Reyes about strongly Oka ideals family. Finally, we characterize the struc- ture of SPAP-ring in special cases.
Communications in Algebra, 2018
A nonzero module M over a commutative ring R is said to have a complete comaximal decomposition i... more A nonzero module M over a commutative ring R is said to have a complete comaximal decomposition if it can be written in the form , where the annihilators of the Ni’s are pairwise comaximal pseudo-irreducible ideals of R. In this paper, we show that a complete comaximal decomposition for an R-module is unique if it exists and a ring R is J-Noetherian if and only if every nonzero R-module has a complete comaximal decomposition. Also, we give a topological characterization of (finitely generated) comultiplication R-modules whose submodules have a complete comaximal decomposition and then we show that a commutative ring R is von Neumann regular if and only if every representable R-module can be written as a finite direct sum of homogeneous semi-simple R-modules.
Communications in Algebra, 2020
Matlis showed that an injective module over a commutative Noetherian ring R can be completely dec... more Matlis showed that an injective module over a commutative Noetherian ring R can be completely decomposed as a direct sum of indecomposable injective submodules. In this paper, we prove the Matlis' Theorem for almost Dedekind domains. Then we characterize the secondary modules and classify the indecomposable secondary modules over almost Dedekind domains. Also we prove every P-secondary module over an almost Dedekind domain is pure-injective, where P 6 ¼ 0: Finally, we characterize the representable finitely generated modules over almost Dedekind domains.
A characterization of commutative rings whose maximal ideal spectrum is Noetherian
Journal of Algebra and Its Applications, 2017
An ideal [Formula: see text] of a ring [Formula: see text] is called pseudo-irreducible if [Formu... more An ideal [Formula: see text] of a ring [Formula: see text] is called pseudo-irreducible if [Formula: see text] cannot be written as an intersection of two comaximal proper ideals of [Formula: see text]. In this paper, it is shown that the maximal spectrum of [Formula: see text] is Noetherian if and only if every proper ideal of [Formula: see text] can be expressed as a finite intersection of pseudo-irreducible ideals. Using a result of Hochster, we characterize all [Formula: see text] quasi-compact Noetherian topological spaces.
Communications in Algebra, 2016
A proper ideal of a commutative ring is called pseudo-irreducible if it cannot be written as a pr... more A proper ideal of a commutative ring is called pseudo-irreducible if it cannot be written as a product of two comaximal proper ideals. In this paper, we give a necessary and su cient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal pseudo-irreducible ideals. Examples of such rings include Laskerian rings, or more generally J-Noetherian rings and ZD-rings. We study when certain classes of rings satisfy this condition.
TURKISH JOURNAL OF MATHEMATICS, 2016
In this paper, by giving an example we answer positively the question "Does there exist a P-prima... more In this paper, by giving an example we answer positively the question "Does there exist a P-primary ideal I in a Noetherian domain R such that P I = I 2 , but I is not almost prime?", asked by S. M. Bhatwadekar and P. K. Sharma. We also investigated conditions under which the answer to the above mentioned question is negative.
A Prime Submodule Principle
Algebra Colloquium, 2014
In this paper, we extend the concept of Ako and Oka families to submodules, study the behavior of... more In this paper, we extend the concept of Ako and Oka families to submodules, study the behavior of the extended prime submodule principle and use these concepts to give new proofs of some familiar theorems.
Iranian Journal of Mathematical Sciences and Informatics, 2018
Let R be a commutative ring and I an ideal of R. The zerodivisor graph of R with respect to I, de... more Let R be a commutative ring and I an ideal of R. The zerodivisor graph of R with respect to I, denoted by ΓI(R), is the simple graph whose vertex set is {x ∈ R \ I | xy ∈ I, for some y ∈ R \ I}, with two distinct vertices x and y are adjacent if and only if xy ∈ I. In this paper, we state a relation between zero-divisor graph of R with respect to an ideal and almost prime ideals of R. We then use this result to give a graphical characterization for SPAP -rings.
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Papers by esmaeil rostami