in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

We characterize mildly mixing group actions of a noncompact locally compact second countable group G using orbit equivalence We show an amenable action of G is mildly mixing if and only if G is amenable and for any nonsingular ergodic G action the product G action is orbit equivalent to We extend the result to the case of nite measure preserving noninvertible endomorphisms i e when G N and show...

This paper focuses on isogeny representations, defined as ways to evaluate isogenies and verify membership the language of isogenous supersingular curves (the set triples $$D,E_1,E_2$$ with a cyclic degree D between $$E_1$$ $$E_2$$ ). The tasks evaluating verifying are fundamental for isogeny-based cryptography. Our main contribution is design suborder representation, new representation targett...

We consider finite additive cellular automata with fixed and periodic boundary conditions as endomorphisms over pattern spaces. A characterization of the nilpotent and regular parts of these endomorphisms is given in terms of their minimal polynomials. We determine the generalized eigenspace decomposition, and describe relevant cyclic subspaces in terms of symmetries. As an application, we calc...

Suppose Dl and D2 be Riemann surfaces which have bounded nonconstant holomorphic functions. Denote by E ( D i ) , i = 1 , 2 , the semigroups of all holomorphic endomorphisms. If $ : E ( D 1 ) + E(D2) is an isomorphism of semigroups then there exists a conformal or anticonformal isomorphism r/l: Dl 3 D2 such that $ is the conjugation by r/l . Also the semigroup of injective endomorphisms as well...

Let P be a partially ordered set. A function φ : P → P is an endomorphism of P if for every two elements x, y of P , the inequality φ(x) 6 φ(y) holds whenever x 6 y. Obviously, the identity mapping is a (trivial ) endomorphism. Here, however, we will be interested in endomorphisms with an image of size less than |P |, i.e. endomorphisms which are not automorphisms of P . We will refer to them a...

Sierpiński proved that every countable set of mappings on an infinite set X is contained in a 2-generated subsemigroup of the semigroup of all mappings on X. In this paper we prove that every countable set of endomorphisms of an algebra A which has an infinite basis (independent generating set) is contained in a 2-generated subsemigroup of the semigroup of all endomorphisms of A.