let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

Let R be a commutative ring with 1 such that Nil(R) is a divided prime ideal of R. The purpose of this paper is to introduce a new class of rings that is closely related to the class of Noetherian rings. A ring R is called a Nonnil-Noetherian ring if every nonnil ideal of R is finitely generated. We show that many of the properties of Noetherian rings are also true for Nonnil-Noetherian rings; ...

Let R be a commutative noetherian ring. We study the behavior of injectiveand at dimension of R-modules under the functors HomR(-,-) and -×R-.

Let R be a Noetherian local ring and Ω an arbitrary R-module of finite depth and finite projective dimension. The flat dimension of Ω is at least depth(R)−depth(Ω) with equality in the following cases: (i) Ω is finitely generated over some Noetherian local R-algebra S; (ii) dim(R) = 1; (iii) dim(R) = 2 and Ω is separated; (iv) R is CohenMacaulay, dim(R) = 3 and Ω is complete.

We study skew inverse power series extensions R[[y−1; τ, δ]], where R is a noetherian ring equipped with an automorphism τ and a τ -derivation δ. We find that these extensions share many of the well known features of commutative power series rings. As an application of our analysis, we see that the iterated skew inverse power series rings corresponding to nth Weyl algebras are complete, local, ...

We study centralizers of elements in domains. We generalize a result of the author and Small [4], showing that if A is a finitely generated noetherian domain and a ∈ A is not algebraic over the extended centre of A then the centralizer of a has Gelfand-Kirillov dimension at most one less than the Gelfand-Kirillov dimension of A. In the case that A is a finitely generated noetherian domain of GK...

Let k be a field. We show that a finitely generated simple Goldie k-algebra of quadratic growth is noetherian and has Krull dimension 1. Thus a simple algebra of quadratic growth is left noetherian if and only if it is right noetherian. As a special case, we see that if A is a finitely generated simple domain of quadratic growth then A is noetherian and by a result of Stafford every right and l...