This article is closely related to that of Eisenbud, Riemenschneider, and Schreyer, where a
universal resolution for certain factor-rings of the symmetric algebra S= S (E) of a projective …

As a generalization of the notion of Frobenius algebras over a field Kasch [103 introduced
that of Frobenius extensions of a ring. The present writers [13] recently freed one of Kasch's …

Since Bass' original paper [5] on injective resolutions and Gorenstein rings, there has been
a number of papers following a similar theme. Perhaps the most notable is the paper of …

Recently Buchsbaum and Eisenbud [3] exploited the algebra structure on a finite free
resolution of a Gorenstein ideal of codimension three to obtain a complete determinantal …

An algebra A, with identity, finite dimensional over a field K, in which the right regular
representation is equivalent to the left regular repre-sentation, is called a Frobenius algebra …

The problem of explicitly finding a free resolution, minimal in some suitable sense, of a
module over a polynomial ring is solved in principle by the algorithm of Hilbert [H]. However …

It is known that a unique factorization domain which is a Cohen-Macaulay factor ring of a
regular local ring is Gorenstein ((221, see, however,[23]). In this paper we show that …

In his paper [1] F. Kasch developed a theory of Frobenius extensions as a generalization of
the theory of Frobenius algebras. In it he established a very interesting relationship between …

In this paper we prove two criteria for a local Cohen-Macaulay ring to be Gorenstein. For the
first criterion we use a condition on Ext-groups of certain locally factorial rings (Theorem2. 1) …

Abstract In Commutative Algebra structure results on minimal free resolutions of Gorenstein
modules are of classical interest. We define Symmetrically Gorenstein modules of finite …