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 …

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 …

Let R=⊕ n∈ ℤ 0 R n be a positively graded ring which is a sub-ring of strongly graded ring
of type ℤ, where R 0 is a Noetherian prime ring. We define a concept of ℤ 0-invariant …

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) …

Generalized Rees rings over Dedekind rings were introduced in [3] as a particular case of
graded Dedekind rings. It was discovered soon that these rings simplified the study of …

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 …

Let R be a maximal order and A, B be R-ideals of R. Clearly (AB)∗⊇ B∗ A∗ is satisfied and
if R is a Dedekind prime ring, the equality holds, ie,(AB)∗= B∗ A∗. However, the equality is …

Full article: Ore Extensions Over PI G-Dedekind Prime Rings Skip to Main Content Taylor and
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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 …

For any pair (n′, k′) of positive integers we produce a strongly Z2-graded ring R such that
the identity component R0 has invariant basis number while the basis-number type of R is …