We develop the representation theory of selfinjective algebras of strictly canonical type and prove that their Auslander-Reiten quivers admit quasi-tubes maximally saturated by simple and projective modules.
We classify all tame self/injective algebras having simply connected Galois coverings and the stable Auslander-Reiten quivers consisting of stable tubes. Moreover, the classification of nondomestic polynomial growth standard self/injective algebras is completed.
We develop the representation theory of selfinjective algebras which admit Galois coverings by the repetitive algebras of algebras whose derived category of bounded complexes of finite-dimensional modules is equivalent to the derived category of coherent sheaves on a weighted projective line with virtual genus greater than one.
This paper owes its origins to Pere Menal and his work on Von Neumann Regular (= VNR) rings, especially his work listed in the bibliography on when the tensor product K = A ⊗K B of two algebras over a field k are right self-injective (= SI) or VNR. Pere showed that then A and B both enjoy the same property, SI or VNR, and furthermore that either A and B are algebraic algebras over k (see [M]). This is connected with a lemma in the proof of the Hilbert Nullstellensatz, namely a finite ring extension...
In this paper, we introduce a new kind of rings that behave like semicommutative rings, but satisfy yet more known results. This kind of rings is called -semicommutative. We prove that a ring is -semicommutative if and only if is -semicommutative if and only if is -semicommutative. Also, if is -semicommutative, then is -semicommutative. The converse holds provided that is nilpotent and is power serieswise Armendariz. For each positive integer , is -semicommutative if and...
Abhyankar proved that every field of finite transcendence degree over or over a finite field is a homomorphic image of a subring of the ring of polynomials (for some depending on the field). We conjecture that his result cannot be substantially strengthened and show that our conjecture implies a well-known conjecture on the additive idempotence of semifields that are finitely generated as semirings.