Maryam Salimi

AMALGAMATED DUPLICATION OF SOME SPECIAL RINGS

Abstract. Let R be a commutative Noetherian ring and let I be anideal of R . In this paper we study the amalgamated duplication ring R ▷◁ I which is introduced by D’Anna and Fontana. It is shown thatif R is generically Cohen-Macaulay (resp. generically Gorenstein) and I is generically maximal Cohen-Macaulay (resp. generically canonicalmodule), then R ▷◁ I is generically Cohen-Macaulay (resp. genericallyGorenstein). We also de ned generically quasi-Gorenstein ring and weinvestigate when R ▷◁ I is generically quasi-Gorenstein. In addition, itis shown that R ▷◁ I is approximately Cohen-Macaulay if and only if R is approximately Cohen-Macaulay, provided some special conditions.Finally it is shown that if R is approximately Gorenstein, then R ▷◁ I isapproximately Gorenstein. 1. IntroductionThroughout this paper all rings are considered commutative with identityelement and all ring homomorphisms are unital. In [8], D’Anna and Fontanaconsidered a fft type of construction obtained involving a ring

Tensor and Torsion Products of Relative Injective Modules with Respect to a Semidualizing Module

Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In this paper, we show that C is generically dualizing if and only if the tensor products of injective and C-injective R-modules are injective. This leads to a characterization of dualizing modules as well as generalizes a result of Enochs and Jenda.

A survey on factors influencing the use of news graphics in Iranian online media

News Graphic is a kind of Infographic which reports the news visually. The difference between news graphic and infographic lies in the content and the speed with which they are presented. Although this kind of graphic is frequently used in media around the world, its use is limited in Iran. The present article aims to study the influential factors in the use of news graphics in Iranian media by means of descriptive methods (interviews and analysis). It has found five deterrent factors including high cost of producing news graphics, low familiarity of media managers with news graphics, limited experience and competence of the Iranian graphic designers in this field, technical and communicational limitations, and the problem of producing and supporting Persian graphical software due to lack of professional groups in creating such software.

Family of quotients of some special rings

Let R be a commutative Noetherian ring and let I≠0 be a proper ideal of R. We study some properties of a family of rings R(I)a,b that are obtained as quotients of the Rees algebra associated with t...

Relative Gorenstein injective covers with respect to a semidualizing module

Let R be a commutative Noetherian ring and let C be a semidualizing R-module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to C which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every GC-injective module G, the character module G+ is GC-flat, then the class

Gorenstein Homological Dimension with Respect to a Semidualizing Module and a Generalization of a Theorem of Bass

\mathcal{GI}_{C}(R)\cap\mathcal{A}_C(R)

A CONSTRUCTION OF QUASI-GORENSTEIN RINGS

GIC(R)∩ n AC(R) is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class