6 papers
A criterion for rings which are locally valuation
Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi
Using the notion of cyclically pure injective modules, a characterization for rings which are locally valuation is established. As applications, new characterizations for Prufer do…
Gorenstein homological dimensions and Auslander categories
Mohammad Ali Esmkhani, Massoud Tousi
In this paper, we study Gorenstein injective, projective, and flat modules over a Noetherian ring . For an -module , we denote by and the Go…
Some criteria of cyclically pure injective modules
Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi
The structure of cyclically pure injective modules over a commutative ring is investigated and several characterizations for them are presented. In particular, we prove that a…
Two characterizations of pure injective modules
Divaani-Aazar, Esmkhani, Tousi
Let be a commutative ring with identity and an -module. It is shown that if is pure injective, then is isomorphic to a direct summand of the direct product of a…
Artinianness of local cohomology modules of ZD-modules
Kamran Divaani-Aazar, Mohammad Ali Esmkhani
This paper centers around Artinianness of the local cohomology of -modules. Let $\fa$ be an ideal of a commutative Noetherian ring . The notion of $\fa$-relative Goldie dime…
Associated prime submodules of finitely generated modules
Kamran Divaani-Aazar, Mohammad Ali Esmkhani
Let be a commutative ring with identity. For a finitely generated -module , the notion of associated prime submodules of is defined. It is shown that this notion inhe…