Semidualizing Modules and Rings of Invariants
William Sanders
TL;DR
This paper proves that nonmodular rings of invariants of order p^n do not admit nontrivial semidualizing modules, clarifying the structure of these algebraic objects.
Contribution
It establishes the nonexistence of nontrivial semidualizing modules for a class of invariant rings, advancing understanding in invariant theory and module theory.
Findings
No nontrivial semidualizing modules exist for these rings
Results apply specifically to rings of invariants of order p^n
Provides new insights into the structure of invariant rings
Abstract
We show there exist no nontrivial semidualizing modules for nonmodular rings of invariants of order with a prime.
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