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On Cohen-Macaulayness and depth of ideals in invariant rings
We investigate the presence of Cohen-Macaulay ideals in invariant rings and
show that an ideal of an invariant ring corresponding to a modular
representation of a -group is not Cohen-Macaulay unless the invariant ring
itself is. As an intermediate result, we obtain that non-Cohen-Macaulay
factorial rings cannot contain Cohen-Macaulay ideals. For modular cyclic groups
of prime order, we show that the quotient of the invariant ring modulo the
transfer ideal is always Cohen-Macaulay, extending a result of Fleischmann.Comment: 9 page
Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type
In this paper we show a partial answer the a question of C. Huneke and G.
Leuschke (2003): Let R be a standard graded Cohen-Macaulay ring of graded
countable Cohen-Macaulay representation type, and assume that R has an isolated
singularity. Is R then necessarily of graded finite Cohen-Macaulay
representation type? In particular, this question has an affirmative answer for
standard graded non-Gorenstein rings as well as for standard graded Gorenstein
rings of minimal multiplicity. Along the way, we obtain a partial
classification of graded Cohen-Macaulay rings of graded countable
Cohen-Macaulay type.Comment: 15 Page
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