We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.
Let be an abelian group, a commutative ring of prime characteristic with identity and a commutative twisted group ring of over . Suppose is a fixed prime, and are the -components of and of the unit group of , respectively. Let be the multiplicative group of and let be the -th Ulm-Kaplansky invariant of where is any ordinal. In the paper the invariants , , are calculated, provided . Further, a commutative ring with identity of prime characteristic is said...
Let G be a noncyclic abelian p-group and K be an infinite field of finite characteristic p. For every 2-cocycle λ ∈ Z²(G,K*) such that the twisted group algebra is of infinite representation type, we find natural numbers d for which G has infinitely many faithful absolutely indecomposable λ-representations over K of dimension d.