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ON PRIME SUBMODULES OF A FINITELY GENERATED PROJECTIVE MODULE OVER A COMMUTATIVE RING
Nekooei, Reza,Pourshafiey, Zahra Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.3
In this paper we give a full characterization of prime submodules of a finitely generated projective module M over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of a finitely generated projective module and characterize the minimal primary decomposition of this submodule. Finally, we characterize the radical of an arbitrary submodule of a finitely generated projective module M and study submodules of M which satisfy the radical formula.
A CHARACTERIZATION OF PRIME SUBMODULES OF AN INJECTIVE MODULE OVER A NOETHERIAN RING
Nekooei, Reza,Pourshafiey, Zahra Korean Mathematical Society 2019 대한수학회보 Vol.56 No.1
In this paper, we give a characterization of prime submodules of an injective module over a Noetherian ring.
A TORSION GRAPH DETERMINED BY EQUIVALENCE CLASSES OF TORSION ELEMENTS AND ASSOCIATED PRIME IDEALS
Reza Nekooei,Zahra Pourshafiey Korean Mathematical Society 2024 대한수학회보 Vol.61 No.3
In this paper, we define the torsion graph determined by equivalence classes of torsion elements and denote it by A<sub>E</sub>(M). The vertex set of A<sub>E</sub>(M) is the set of equivalence classes {[x] | x ∈ T(M)<sup>*</sup>}, where two torsion elements x, y ∈ T(M)<sup>*</sup> are equivalent if ann(x) = ann(y). Also, two distinct classes [x] and [y] are adjacent in A<sub>E</sub>(M), provided that ann(x)ann(y)M = 0. We shall prove that for every torsion finitely generated module M over a Dedekind domain R, a vertex of A<sub>E</sub>(M) has degree two if and only if it is an associated prime of M.
A characterization of prime submodules of an injective module over a Noetherian ring
Reza Nekooei,Zahra Pourshafiey 대한수학회 2019 대한수학회보 Vol.56 No.1
In this paper, we give a characterization of prime submodules of an injective module over a Noetherian ring.
On Representable Rings and Modules
Reza Nekooei,Seyed Ali Mousavi,Fatemeh Mirzaei 경북대학교 자연과학대학 수학과 2022 Kyungpook mathematical journal Vol.62 No.3
In this paper, we determine the structure of rings that have secondary repre sentation (called representable rings) and give some characterizations of these rings. Also, we characterize Artinian rings in terms of representable rings. Then we introduce com pletely representable modules, modules every non-zero submodule of which have secondary representation, and give some necessary and sufficient conditions for a module to be com pletely representable. Finally, we define strongly representable modules and give some conditions under which representable module is strongly representable.
ON PRIME SUBMODULES OF AN INJECTIVE MODULE OVER A NOETHERIAN RING
( Zahra Pourshafiey And Reza Nekooei ) 호남수학회 2018 호남수학학술지 Vol.40 No.2
In this paper, we characterize the prime submodules of an injective module over a Noetherian ring.
ON PRIME SUBMODULES OF AN INJECTIVE MODULE OVER A NOETHERIAN RING
Pourshafiey, Zahra,Nekooei, Reza The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.2
In this paper, we characterize the prime submodules of an injective module over a Noetherian ring.
CHARACTERIZATION OF PRIME SUBMODULES OF A FREE MODULE OF FINITE RANK OVER A VALUATION DOMAIN
Mirzaei, Fatemeh,Nekooei, Reza Korean Mathematical Society 2017 대한수학회지 Vol.54 No.1
Let $F=R^{(n)}$ be a free R-module of finite rank $n{\geq}2$. In this paper, we characterize the prime submodules of F with at most n generators when R is a $Pr{\ddot{u}}fer$ domain. We also introduce the notion of prime matrix and we show that when R is a valuation domain, every finitely generated prime submodule of F with at least n generators is the row space of a prime matrix.
Effect of Dry and Saturated Bentonite on Plastic Concrete
Mohammad Amin Fadaie,Masoud Nekooei,Pasha Javadi 대한토목학회 2019 KSCE JOURNAL OF CIVIL ENGINEERING Vol.23 No.8
Dams are rarely built on non-permeable lands, therefore usually reservoir leakage from dam foundations cause major problems for large dams which affect dams performances. One method of controlling the origin of leaks is to use plastic concrete cutoff walls. Bentonite is one of the most important materials used in constructing plastic concrete which act as a stabilizing agent. It is from clay materials having high water absorption and swelling of 300% properties even after contacting with water. These properties may cause negative effects on plastic concretes that include deep cracks and high reductions on its strength. In order to eliminate these effects, plastic concretes must be mixed with water at least 24 hours before usage and then they must be blended by special blades until they are totally saturated. This process costs huge time and money. Therefore, in this research, dry bentonite has been added to the mixer with particular method. It can be seen saving time and money and the properties of plastic concrete such as compressive strength, tensile strength, slump and permeability will not be slightly changed.
Seismic behavior of steel column-base-connection equipped by NiTi shape memory alloy
Reza Jamalpour,Masoud Nekooei,Abdolreza Sarvghad Moghadam 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.64 No.1
The behavior of moment resistant steel structures depends on both the beam-column connections and columns foundations connections. Obviously, if the connections can meet the adequate ductility and resistance against lateral loads, the seismic capacity of these structures will be linked practically to the performance of these connections. The shape memory alloys (SMAs) have been most recently used as a means of energy dissipation in buildings. The main approach adopted by researchers in the use of such alloys is firstly bracing, and secondly connecting the beams to columns. Additionally, the behavior of these alloys is modeled in software applications rarely involving equivalent torsional springs and column-foundation connections. This paper attempts to introduce the shape memory alloys and their applications in steel structural connections, proposing a new steel column- foundation connection, not merely a theoretical model but practically a realistic and applicable model in structures. Moreover, it entails the same functionality as macro modeling software based on real behavior, which can use different materials to establish a connection between the columns and foundations. In this paper, the suggested steel column-foundation connection was introduced. Moreover, exploring the seismic dynamic behavior under cyclic loading protocols and the famous earthquake records with different materials such as steel and interconnection equipment by superelastic shape memory alloys have been investigated. Then, the results were compared to demonstrate that such connections are ideal against the seismic behavior and energy dissipation.