Locally quasi-unmixed Noetherian rings and ideals of the principal class

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

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...

Artinian and Noetherian Rings

Graphs and principal ideals of finite commutative rings

In [1], Afkhami and Khashyarmanesh introduced the cozero-divisor graph of a ring, Γ′(R), which examines relationships between principal ideals. We continue investigating the algebraic implications of the graph by developing the reduced cozero-divisor graph, which is a simpler analog. Acknowledgements: This research was undertaken at the Wabash College Mathematics REU in Crawfordsville, Indiana....