Let Γ denote a group of finite virtual cohomological dimension and p a prime. If the cohomology ring H∗(Γ;Fp) has Krull dimension one, the p-period of Γ is defined; it measures the periodicity of H∗(Γ;Fp) in degrees above the virtual cohomological dimension of Γ. The Yagita invariant p(Γ) of Γ is a natural generalization of the p-period to groups with H∗(Γ;Fp) of Krull dimension larger than one...

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, ...

The notion of deviation of an ordered set has been introduced by Gabriel as a tool to classify rings. It measures how far a given ordered set P deviates from ordered sets satisfying the descending chain condition. We consider here a more general notion and, according to Robson, we define the Krull dimension of P as the deviation of the collection F(P) of its final segments ordered by inclusion....

Given an ideal a in A[x1, . . . , xn] where A is a Noetherian integral domain, we propose an approach to compute the Krull dimension of A[x1, . . . , xn]/a, when the residue class ring is a free A-module. When A is a field, the Krull dimension of A[x1, . . . , xn]/a has several equivalent algorithmic definitions by which it can be computed. But this is not true in the case of arbitrary Noetheri...

let $r$ be a commutative ring with identity and let $m$ be an $r$-module. a proper submodule $p$ of $m$ is called strongly prime submodule if $(p + rx : m)ysubseteq p$ for $x, yin m$, implies that $xin p$ or $yin p$. in this paper, we study more properties of strongly prime submodules. it is shown that a finitely generated $r$-module $m$ is artinian if and only if $m$ is noetherian and every st...

It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self f p-injective, zero-Krull dimensional, CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commu-tative arithmetic ring is a Kaplansky r...