F-injectivity and Frobenius closure of ideals in Noetherian rings of characteristic p> 0

On p-injectivity, YJ-injectivity and quasi-Frobeniusean rings

A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

On Prime Ideals of Noetherian Skew Power Series Rings

We study prime ideals in skew power series rings T := R[[y; τ, δ]], for suitably conditioned complete right noetherian rings R, automorphisms τ of R, and τ -derivations δ of R. Such rings were introduced by Venjakob, motivated by issues in noncommutative Iwasawa theory. Our main results concern “Cutting Down” and “Lying Over.” In particular, assuming that τ extends to a compatible automorphsim ...

Q–gorenstein Splinter Rings of Characteristic P Are F–regular

A Noetherian integral domain R is said to be a splinter if it is a direct summand, as an R–module, of every module–finite extension ring, see [Ma]. In the case that R contains the field of rational numbers, it is easily seen that R is splinter if and only if it is a normal ring, but the notion is more subtle for rings of characteristic p > 0. It is known that F–regular rings of characteristic p...

D-Bases for Polynomial Ideals over Commutative Noetherian Rings

On Some Characteristic Properties of Quasi-frobenius and Regular Rings

Recently the first writer [l] gave a characterization of quasiFrobenius rings, introduced formerly by the second writer [3], in terms of a condition proposed by K. Shoda, which reads: A ring A satisfying minimum condition and possessing a unit element is a quasi-Frobenius ring if and only if A satisfies the following condition:1 (a) every (A -left-) homomorphism of a left-ideal of A into A may ...