Let R be a ring, let G be a countable amenable group and let RG be a crossed product. The
goal of this paper is to construct, starting with a suitable length function L on the category of …

Let R be a ring, let G be an amenable group and let R* GR∗ G be a crossed product. The
goal of this paper is to construct, starting with a suitable additive function L on the category of …

The Pinsker subgroup of an abelian group G with respect to an endomorphism φ of G was
introduced in the context of algebraic entropy. Motivated by the nice properties and …

Three new results on the algebraic entropy are presented. The first result removes one of the
sufficient conditions for the uniqueness of the algebraic L-entropy, where L is a length …

We extend the notion of intrinsic entropy for endomorphisms of Abelian groups to
endomorphisms of modules over an Archimedean non-discrete valuation domain R, using …

We describe the framework for the notion of a restricted inverse limit of categories, with the
main motivating example being the category of polynomial representations of the group …

We partially generalize Peters' formula [Adv. in Math. 33 (1979), pp. 1–13] on modules over
the group ring $\mathbb {F}\Gamma $ for a given finite field $\mathbb {F} $ and a sofic group …

Inspired by the work of Crawley-Boevey on additive functions in locally finitely presented
Grothendieck categories, we describe a natural way to extend a given exact Sylvester rank …

Recall that a module X over some associative ring R is endofinite if X has finite length when
viewed as a module over its endomorphism ring EndR (X). Such modules have been …

LetRbe a ring, Pbe a∗-module, andS= EndP. Inspired by the tilting theory, we investigate
relations between the global dimensions gldimRand gldimS, and between the structure of …