Kazuho Ozeki

Ulrich ideals and modules

In this paper we study Ulrich ideals of and Ulrich modules over Cohen–Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and classify Ulrich ideals of numerical semigroup rings and rings of finite CM-representation type.

The structure of Sally modules and Buchsbaumness of associated graded rings

Let A be a Noetherian local ring with the maximal ideal m, and let I be an m-primary ideal in A . This paper examines the equality on Hilbert coefficients of I first presented by Elias and Valla, but without assuming that A is a Cohen–Macaulay local ring. That equality is related to the Buchsbaumness of the associated graded ring of I .