Gorenstein injective and projective modules and actions of finite-dimensional Hopf algebras

By Theorem 5.3, Spec R has a one-parameter equisingular deformation, obtained from blowing down an equisingular deformation of X for which the induced deformation of

This is a special case of the result to be proved in this paper as minimally elliptic singularities are Gorenstein surface singularities x with embedding

The question arises as to when a semi-simple near-ring is strictly semi-simple (the converse clearly is always true). case a module M is injective iff it satisfies

In Section 3, after discussing pertinent facts concerning dualizing modules and Gorenstein modules, we turn to a problem related to the central res alt of Section i, namely: If A is

We give a relationship between injective cogenerators (resp., projective generators) introduced by Sather-Wagstaff, Sharif and White and CE-injective CE-cogen- erators

A ring R is right coherent if and only if every R-module has a flat preenvelope [10, Proposition 6.5.1], and by Theorem 4.2, if and only if every complex of R-modules has

(2) In Lemma 17 and Proposition 18 we showed that the space V d is spanned by the Specht polynomials defined by the standard Young tableau of shape (k d; d).. It is well known that

In section 0 we recall some basic notions of graded ring and module theory. it has a unique maximal ideal).. After that, the characterization of Cohen-Macaulay and