Semidualizing modules and rings of invariants

Abstract

Abstract. We show there exist no nontrivial semidualizing modules for nonmodular rings of invariants of order p n with p a prime.

On semidualizing modules of ladder determinantal rings

“…Anders Frankild and Sather-Wagstaff show that the set has even cardinality when R is local, complete, Cohen-Macaulay, and not Gorenstein in [7]. At this time, we only have more information than this in very special cases: Olgur Celikbas and Hailong Dao [2] deal with certain Veronese subrings; William Sanders [13] handles some rings of invariants; Sather-Wagstaff treats determinantal rings in [14]; and Nasseh, Sather-Wagstaff, and Ryo Takahashi [10,11] handle the rings that specialize to non-trivial fiber products (this includes the well-known but seemingly undocumented result for rings of minimal multiplicity).…”