It is well-known that for a lattice-finite order Λ over a complete discrete valuation domain, the
radical of Λ-lat (the category of Λ-lattices) is nilpotent modulo projectives. Iyama has shown …

We study the relationship between representation theoretic properties and homological
properties of orders. We show that there is a close relationship among Auslander orders, τ …

In this paper, we study lattices of preradicals which are not small classes (in which case we
say that the corresponding rings are p-large), and specially we consider some infinite …

Let ℒ be an n-dimensional restricted Lie algebra over an algebraically closed field K of
characteristic p> 0. Given a linear function ξ on ℒ and a scalar λ∈ K, we introduce an …

We describe in the paper the graded centers of the bounded derived categories of the
derived discrete algebras. In particular, we prove that if A is a derived discrete algebra, then …

The singularity category of a ring makes only the modules of finite projective dimension
vanish among the modules, so that the singularity category is expected to characterize a …

We introduce a new family of algebras, called Serre-formal algebras. They are Iwanaga–
Gorenstein algebras for which applying any power of the Serre functor on any …

Historically, the study of modules over finite dimensional algebras has started with the study
of the ones with finite dimension. This is sufficient when dealing with a finite dimensional …

Abstract Let $\mathfrak {g}=\mathfrak {g}\mathfrak {l} _ {N}(\Bbbk) $, where $\Bbbk $ is an
algebraically closed field of characteristic $ p> 0$, and $ N\in\mathbb {Z} _ {{\geqslant} 1} …

Let A be an artin algebra and mod A the category of finitely generated left A-modules.
Denote by rad (mod A) the Jacobson radical of mod A and by rad*(mod A) the infinite radical …