Gorenstein rings with semigroup bases
The author develops the module theory over non-semiprime QF-3, 1- Gorenstein rings with zero socle. First the author proves that if R is a discrete valuation ring and S is a semi-Kupisch semigroup which is Frobenius with respect to R, then the semigroup ring R[S] is a QF-3, 1- Gorenstein ring with zero socle. In order to study the module theory, the author introduces the notions of ring frame and frame ring over a semi- Kupisch semigroup. Then he proves that if \(\Lambda\) is a QF-3, 1- Gorenstein ring with zero socle, then any injective indecomposable \(\Lambda\) -module E is either torsionfree or torsion with respect to the Lambek torsion theory. And he also investigates finitely generated torsion modules over a Kupisch ring and finitely generated torsionfree modules over a strongly Kupisch ring.
scientific article; zbMATH DE number 3875470
scientific article