We present a unifying approach to the study of entropies in Mathematics, such as measure
entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account …

We study the receptive metric entropy for semigroup actions on probability spaces, inspired
by a similar notion of topological entropy introduced by Hofmann and Stoyanov (Adv Math …

A left semigroup action SÕ A of a semigroup S on an abelian group A (by group
endomorphisms) is defined by WSA! A,. s; x/7!. s/. x/with. st/D. s/ı. t/and. s/. x C y/D. s/. x/C. s …

The notion of entropy appears in many branches of mathematics. In each setting (eg,
probability spaces, sets, topological spaces) entropy is a non-negative real-valued function …

Let $ G $ be a countable cancellative amenable semigroup and let $(F_n) $ be a (left) F {\o}
lner sequence in $ G $. We introduce the notion of an $(F_n) $-normal element of $\{0, 1\} …

For a left action S↷ λ X of a cancellative right amenable monoid S on a discrete Abelian
group X, we construct its Ore localization G↷ λ∗ X∗, where G is the group of left fractions of …

Additivity with respect to exact sequences is, notoriously, a fundamental property of the
algebraic entropy of group endomorphisms. It was proved for abelian groups by using the …

We prove the so-called Addition Theorem for the algebraic entropy of actions of cancellative
right amenable monoids S on discrete abelian groups A by endomorphisms, under the …

The usual notion of algebraic entropy associates to every group (monoid) endomorphism a
value estimating the chaos created by the self-map. In this paper, we study the extension of …

Mean dimension may decrease after taking the natural extension. In this paper we show that
mean dimension is preserved by natural extension for an endomorphism on a compact …