A semidualizing module is a generalization of Grothendieck's dualizing
module. For a local Cohen-Macaulay ring R, the ring itself and its canonical
module are always realized as (trivial) semidualizing modules. Reasonably, one
might ponder the question; when do nontrivial examples exist? In this paper, we
study this question in the realm of numerical semigroup rings and completely
classify which of these rings with multiplicity at most 9 possess a nontrivial
semidualizing module. Using this classification, we construct numerical
semigroup rings in any multiplicity at least 9 possesses a nontrivial
semidualizing module.Comment: 22 pages, comments welcom