Let $ R=\oplus_ {\alpha\in G} R_ {\alpha} $ be a commutative ring with unity graded by an
arbitrary grading commutative monoid $ G $. For each positive integer, the notions of a …

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 …

Characterizations of Augmented Graded Rings Page 1 Turkish Journal of Mathematics
Volume 29 Number 3 Article 1 1-1-2005 Characterizations of Augmented Graded Rings …

Let R be a commutative ring with nonzero identity and Γ (or sometimes G) a commutative
monoid. The concept of coherent rings is one of the most significant notions in homological …

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 pseudo 2-prime ideals of graded commutative rings with
nonzero identities. Let G be a commutative additive monoid with an identity element 0, and …

In this paper we introduce and study the notion of a graded 2-nilgood ring which is graded
by a group. We discuss graded group ring and graded matrix ring extensions of graded 2-nil …

Let be a ring graded by an arbitrary grading abelian group Γ. We say that R is a uniformly
graded-coherent ring if there is a map ϕ: ℕ→ ℕ such that for every n∈ ℕ, and any nonzero …

Let R be a G-graded ring. In this article, we introduce two new concepts on graded rings,
namely, weakly graded rings and invertible graded rings, and we discuss the relations …

Let R=⊕ α∈ Γ Rα be a commutative ring graded by an arbitrary torsionless monoid Γ. A
homogeneous prime ideal P of R is said to be strongly homogeneous prime if aP and bR are …