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ON PRIME SUBMODULES OF AN INJECTIVE MODULE OVER A NOETHERIAN RING
Zahra Pourshafiey,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.
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.
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.
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.
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 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.