Self-injective Right Artinian Rings and Igusa Todorov Functions

Artinian and Noetherian Rings

Artinian Band Sums of Rings

Band sums of associative rings were introduced by Weissglass in 1973. The main theorem claims that the support of every Artinian band sum of rings is finite. This result is analogous to the well-known theorem on Artinian semigroup rings. 1991 Mathematics subject classification (Amer. Math. Soc): primary 16P20, 16W50; secondary 20M25. Let B be a band, that is, a semigroup consisting of idempoten...

Self-tests for Freeness over Commutative Artinian Rings

We prove that the Auslander-Reiten conjecture holds for commutative standard graded artinian algebras, in two situations: The first is under the assumption that the modules considered are graded and generated in a single degree. The second is under the assumption that the algebra is generic Gorenstein of socle degree 3.

Pure-injective Modules over Right Noetherian Serial Rings

We give a criterion for the existence of a super-decomposable pure-injective module over an arbitrary serial ring.

Torsionfree Dimension of Modules and Self-injective Dimension of Rings

Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated R-modules. For any n 0, we prove that R is a Gorenstein ring with self-injective dimension at most n if and only if every finitely generated left R-module and every finitely generated right R-module have torsionfree dimension at most n, if and only if every finitely generated le...