… to artin algebras with only minor changes. We begin by giving a definition of Cohen-Macaulay
artin algebras … ring R is Cohen-Macaulay if and only if R has a dualizing module w. If R is a …

… We study Artin algebras Λ and commutative Noetherian complete local rings R in
connection with the following decomposition property of Gorenstein-projective modules: …

… We know there are compressed graded Gorenstein Artin algebras A’ = R/I’ having socle
degree j(A’) = v - 3 = 2d’ - 2, with v = ~(1’) = v(l), defined by Pfaffian ideals I’ = Pf P’ where PIERI …

… of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection
of commutative algebra, singularity theory, and representations of groups and algebras. …

… For the same reason, the completion R is Noetherian and in fact CohenMacaulay of
dimension d, as (uſ,..., ud) remains R-regular (by an argument similar to the one in the proof of …

… in [13] and is mainly devoted to commutative CohenMacaulay algebras. … By a Cohen-Macaulay
algebra over D we mean a D-algebra A which is a … We consider the artin algebra (3.3) …

… an AS-Cohen-Macaulay algebra A has a balanced dualizing complex in the sense of [lo,
Definitions 3.3 and 4.11, if and only if A is graded factor of an AS-Gorenstein algebra. First let us …

… Although an Artin-Schelter Gorenstein algebra is … Artin-Schelter Gorenstein algebras that
are not necessarily connected N-graded. Many examples of Artin-Schelter Gorenstein algebras …

… The same idea can be used for many CohenMacaulay modules (Example 1.1). But although
the Scheja-Storch resolution is minimal in some cases, it is not minimal in the main case of …

… and their indecomposable CohenMacaulay modules. We also assume that R is the center
of A, a complete normal domain of dimension 2. When this is done, AK is a central simple K-…