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.

Finite additive cellular automata with fixed and periodic boundary conditions are considered as endomorphisms over pattern spaces. A characterization of the nilpotent and regular parts of these endomorphisms is given in terms of their minimal polynomials. Generalized eigenspace decomposition is determined and relevant cyclic subspaces are described in terms of symmetries. As an application, the...

Assuming the Mumford–Tate conjecture, we show that center of endomorphism ring an abelian variety defined over a number field can be recovered from appropriate intersection fields obtained its Frobenius endomorphisms. We then apply this result to exhibit practical algorithm compute center.

Previously, we have shown that the CAR algebra for fermions is embedded in the Cuntz algebra O2 in such a way that the generators are expressed in terms of polynomials in the canonical generators of the latter, and it coincides with the U(1)-fixed point subalgebra A ≡ O 2 of O2 for the canonical gauge action. Based on this embedding formula, some properties of A are studied in detail by restric...

Abstract In this paper, we address the problem of computing topological entropy a map $\psi : G \to G$ , where is Lie group, given by some power (g) = g^k$ with k positive integer. When abelian, $ an endomorphism and its $h(\psi ) \dim (T(G)) \log (k)$ $T(G)$ maximal torus as shown Patrão [The endomorphisms groups. Israel J. Math. 234 (2019), 55–80]. However, when not no longer these previous r...

algebra and enumerative combinatorics We learn something when we can interpret combinatorial numbers as orders of algebraic structures, especially groups. Lagrange’s Theorem means that group orders tend to have a rich arithmetic structure. I first learned from Norman’s paper on chip-firing games the fact that the number of spanning trees of a graph is the order of an abelian group canonically a...

In this paper, we initiate the study of endomorphisms and modular theory of the graph C*-algebras Oθ of a 2-graph F + θ on a single vertex. We prove that there is a semigroup isomorphism between unital endomorphisms of Oθ and its unitary pairs with a twisted property. We characterize when endomorphisms preserve the fixed point algebra F of the gauge automorphisms and its canonical masa D. Some ...

We give a detailed account of the use of Q-curve reductions to construct elliptic curves over Fp2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as Gallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) endomorphisms. Like GLS (which is a degenerate case of our construction), we offer the advantage over GLV of ...