Let A be a commutative Noetherian local ring containing a field of characteristic p > 0. The integer invariants λi,j(A) have been introduced in an old paper of ours. In this paper we completely describe λd,d(A) where d = dimA in terms of the topology of SpecA.

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437–445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of modules. Examples over not necessarily Noetherian rings are given.

Let R be a differentiably simple Noetherian commutative ring of characteristic p > 0 (then (R,m) is local with n := emdim(R) < ∞). A short proof is given of the Theorem of Harper [1] on classification of differentiably simple Noetherian commutative rings in prime characteristic. The main result of the paper is that there exists a nilpotent simple derivation of the ring R such that if δ i 6= 0 t...

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; ...

we define and studyco-noetherian dimension of rings for which the injective envelopeof simple modules have finite krull-dimension. this  is a moritainvariant dimension that measures how far the ring is from beingco-noetherian. the co-noetherian dimension of certain rings,including commutative rings, are determined. it is shown that the class ${mathcal w}_n$ of rings with co-noetherian dimension...

 Let $R=oplus_{nin Bbb N_0}R_n$ be a Noetherian homogeneous ring with local base ring $(R_0,frak{m}_0)$, $M$ and $N$ two finitely generated graded $R$-modules. Let $t$ be the least integer such that $H^t_{R_+}(M,N)$ is not minimax. We prove that $H^j_{frak{m}_0R}(H^t_{R_+}(M,N))$ is Artinian for $j=0,1$. Also, we show that if ${rm cd}(R_{+},M,N)=2$ and $tin Bbb N_0$, then $H^t_{frak{m}_0R}(H^2_...

We show that every graded locally finite right noetherian algebra has sub-exponential growth. As a consequence, every noetherian algebra with exponential growth has no finite dimensional filtration which leads to a right (or left) noetherian associated graded algebra. We also prove that every connected graded right noetherian algebra with finite global dimension has finite GK-dimension. Using t...

The purpose of this note is to establish a number of useful results about the augmentation ideal J for the coefficient ring F ∗ G of a Noetherian complex orientable equivariant cohomology theory. The results show that various naturally occurring substitutes for the ideal have the same radical, and can therefore be used instead of the augmentation ideal in all geometric constructions. 1. Stateme...

We define and studyco-Noetherian dimension of rings for which the injective envelopeof simple modules have finite Krull-dimension. This  is a Moritainvariant dimension that measures how far the ring is from beingco-Noetherian. The co-Noetherian dimension of certain rings,including commutative rings, are determined. It is shown that the class ${mathcal W}_n$ of rings with co-Noetherian dimension...

The Noetherian type of a space is the least κ for which the space has a κop-like base, i.e., a base in which no element has κ-many supersets. We prove some results about Noetherian types of (generalized) ordered spaces and products thereof. For example: the density of a product of not-too-many compact linear orders never exceeds its Noetherian type, with equality possible only for singular Noet...