This paper consists of three results on Frobenius categories: (1)we give sufficient conditions on when a factor category of a Frobenius category is still a Frobenius category; (2) we show that any Frobenius category is equivalent to an extension-closed exact subcategory of the Frobenius category formed by Cohen–Macaulaymodules over some additive category; this is an analogue of Gabriel–Quillen’...

This note investigate some finiteness properties of the category U of unstable modules. One shows finiteness properties for the injective resolution of finitely generated unstable modules. One also shows a stabilization result under Frobenius twist for Ext-groups.

Recall that a finite-dimensional commutative associative algebra equipped with an invariant nondegenerate symmetric bilinear form is called a Frobenius algebra (here, we do not require an existence of a unit in Frobenius algebra). Any commutative quasi-Frobenius algebra is always Frobenius, i.e., if the identity ab = ba (commutativity) is fulfilled in a quasi-Frobenius algebra, then the identities

We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assumption for the infinite Frobenius elements in the class groups of these orders.

Let W be a finite Weyl group and σ a non-trivial graph automorphism of W . We show a remarkable relation between the σ-twisted involution module for W and the Frobenius–Schur indicators of the unipotent characters of a corresponding twisted finite group of Lie type. This extends earlier results of Lusztig and Vogan for the untwisted case and then allows us to state a general result valid for an...

Müller generalized in [12] the notion of a Frobenius extension to left (right) quasi-Frobenius extension and proved the endomorphism ring theorem for these extensions. Recently, Guo observed in [9] that for a ring homomorphism φ : R → S, the restriction of scalars functor has to induction functor S ⊗R − : RM → SM as right ”quasi” adjoint if and only if φ is a left quasi-Frobenius extension. In ...

We give an example of an infinite simple Frobenius group G without involutions, with a trivial kernel and a nilpotent complement. Nevertheless, this group is not ωstable (not even superstable), this is the ”only” property missing in order to be a counterexample to the Cherlin-Zil’ber Conjecture which says that simple ωstable groups are algebraic groups.