This article consists of a collection of open problems in commutative algebra. The collection covers a wide range of topics from both Noetherian and non-Noetherian ring theory and exhibits a variety of research approaches, including the use of homological algebra, ring theoretic methods, and star and semistar operation techniques. The problems were contributed by the authors and editors of this...

The theory of mixed multiplicities (not necessarily Noetherian) filtrations mR-primary ideals in a Noetherian local ring R, has been developed by Cutkosky, Sarkar and Srinivasan. objective this article is to generalise Minkowski-type inequality given their paper. We also recover result Srinivasan Verma as simple consequence our inequality.

To reduce to resolving Cohen–Macaulay singularities, Faltings initiated the program of “Macaulayfying” a given Noetherian scheme X. For wide class X, Kawasaki built sought-for modifications, with crucial drawback that his blowups did not preserve locus CM(X)?X, where X is already Cohen–Macaulay. We extend Kawasaki’s methods show every quasi-excellent, has X˜ proper map X˜?X an isomorphism over ...