Powers of ideals in locally unmixed Noetherian rings

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 ...

D-Bases for Polynomial Ideals over Commutative Noetherian Rings

Weak Bourbaki Unmixed Rings: a Step towards Non-noetherian Cohen-macaulayness

Weak Bourbaki unmixed rings are defined in this paper. The definition of a weak Bourbaki unmixed ring is a candidate for an “appropriate” definition of CohenMacaulayness. We will see that this definition satisfies many of the conditions we want an “appropriate” definition to satisfy. It is not yet known whether this definition (or any other) satisfies all of the conditions. However, no example ...

Fully Bounded Noetherian Rings

Let i : A → R be a ring morphism, and χ : R → A a right R-linear map with χ(χ(r)s) = χ(rs) and χ(1 R) = 1 A. If R is a Frobenius A-ring, then we can define a trace map tr : A → A R. If there exists an element of trace 1 in A, then A is right FBN if and only if A R is right FBN and A is right noetherian. The result can be generalized to the case where R is an I-Frobenius A-ring. We recover resul...

Equidimensional and Unmixed Ideals of Veronese Type

This paper was motivated by a problem left by Herzog and Hibi, namely to classify all unmixed polymatroidal ideals. In the particular case of polymatroidal ideals corresponding to discrete polymatroids of Veronese type, i.e ideals of Veronese type, we give a complete description of the associated prime ideals and then, we show that such an ideal is unmixed if and only if it is CohenMacaulay. We...