Representational Repleteness of Differential Operator Rings

Differential Polynomial Rings of Triangular Matrix Rings

Representational Consistency of Group Rings

Received: March 21, 2011 Accepted: April 14, 2011 doi:10.5539/jmr.v3n3p89 Abstract It is shown that if a group ring satisfies the idempotent conjecture and some other restrictions it will be representational consistent. As an application we show the real numbers as a field are representational consistent. This leads to the problem of whether a circle can be given a field structure that can be s...

Tauvel’s Height Formula in Iterated Differential Operator Rings

Let k be a field of positive characteristic, R an associative algebra over k and let ∆1,n = {δ1, . . . , δn} be a finite set of k-linear derivations from R to R. Let A = Rn = R[θ1, δ1] · · · [θn, δn] be an iterated differential operator k-algebra over R such that δj(θi) ∈ Ri−1θi +Ri−1; 1 ≤ i < j ≤ n. As central result we show that if R is noetherian affine ∆1,n-hypernormal and if Tauvel’s heigh...

Localization and Catenarity in Iterated Differential Operator Rings

Let k be a field, R an associative k-algebra with identity, a finite set of derivations of R, and R 1 1 · · · n n an iterated differential operator k-algebra over R such that j i ∈ R 1 1 · · · i−1 i−1 1 ≤ i < j ≤ n. If R is Noetherian -hypercentral, then every prime ideal P of A is classically localizable. The aim of this article is to show that under some additional hypotheses on the -prime id...

differential polynomial rings of triangular matrix rings