Let R=n∈\ZR_n be a strongly graded ring of type \Z and R_0 is a prime Goldie ring. It is
shown that the following three conditions are equivalent:(i) R_0 is a \Z-invariant Krull ring,(ii) …

Let R=⊕ n∈ ℤ R n be a strongly graded ring of type ℤ such that R 0 is a prime Goldie ring
with its quotient ring Q 0. It is shown that the following three conditions are equivalent:(i) R 0 …

. The goal of this article is to present the graded J-ideals of G-graded rings which are
extensions of J-ideals of commutative rings. A graded ideal P of a G-graded ring R is a …

The aim of this note is to give sufficient conditions for a strongly Z-graded ring to be a
Marubayashi-Krull order (cf. Theorem 3.10). Concrete examples of strongly E-graded rings …

A note on graded regular rings Page 1 COMMUNICATIONS IN ALGEBRA, 25(1), 223-228 (1997)
A NOTE ON GRADED REGULAR RINGS Hafizah Yahya Department of Mathematical Sciences …

Graded Rings in which Every Graded Ideal is a Product of Gr-Primary Ideals 1 Introduction
Page 1 International Journal of Algebra, Vol. 2, 2008, no. 16, 779 - 788 Graded Rings in which …

In this paper we study the augmented graded rings and give the ralationship between these
rings and stronger properties of graded rings.

In this paper we study graded rings with an arithmetical ideal theory for the graded ideals,
eg, Gr-Dedekind and Gr-principal ideal rings. If these rings are positively graded rings, then …

The notion of tight closure of an ideal introduced by Hochster and Huneke [5] enables us to
define classes of singularities corresponding to rational singularities in characteristic 0 for …

Let R be a commutative graded ring with nonzero identity and na positive integer. Our
principal aim in this paper is to introduce and study the notions of graded n-irreducible and …