Semigroup Of Endomorphisms Research Articles

On the endomorphism semigroup of simple algebras

On the endomorphism semigroup of simple algebras

Markov branching processes and semigroups of operators

In this paper we study the semigroups of operators associated with Markov branching processes. Our approach is based on the semigroup of operators associated with the generating function of the probabilities of a given branching process. Let F(s, t) = ∑ x = 0 ∞ P x(t)s x, ¦ s ¦ ⩽ 1 , denote the generating function of the probabilities { P x ( t)}. We consider F( s, t), for every fixed t, to be an element of the Hilbert space H 2 of functions analytic in the unit circle, and define an endomorphism T( t) on H 2 as follows: For F( s, t) ϵ H 2, T( t)[ F( s, u)] = F( F( s, t), u) = F( s, t + u). If F( s, 0) = s, then the above becomes F( s, t) = T( t)[ s], It is shown that the family of endomorphisms { T( t), t ⩾ 0} is a semigroup of endomorphisms in H 2 and various properties of the semigroup and its infinitesimal generator are established.

Solution of a problem of G. Grätzer concerning endomorphism semigroups

In this paper a solution of a problem of G. G~TZEI~ [1] (Problem 17) is given, To formulate the problem let 9.1 be a universal algebra (briefly: algebra) and let ~2 (9. 0, 932 (92), 5) (92) be the semigroups of the endomorphisms, monomorphisms, and epimorphisms of 9J, respectively. The problem is to characterize the triplets (~(~), 932(~I), ~(gj)) in terms of the theory of semigroups. G. GR~TZER gives in [1] certain conditions necessary for a given triplet (E, M, H) of semigroups to be isomorphic with some triplet (~(~.I), 9Jl(92), ~)(~l)) (see w 1, Theorem, conditions C1--C3, in this paper). E. FR~D and (later) the author found a further necessary condition, independent of the former ones (condition C4). Conditions C1--C4 are jointly sufficient; consequently, these give the solution of the problem. In w 1 we fix some necessary notions, formulate the theorem, prove the necessitystatement of it and outline the construction, serving to prove the sufficiencystatement. In w 2 we describe the latter construction in detail and give, as corollaries of the theorem, solutions of Problem 16 in [1] concerning the characterization of the couples (@(9.I), 93l(92)) and the corresponding problem for epimorphisms. I must express my gratitude to MR. GEORGE GR~TZER for his valuable remarks in connection with this paper.

Some automorphisms of finite nilpotent groups

This note extends the concept of the inner automorphism, but here applies only to those finite groups G for which some member of the lower central series is Abelian. In general (e.g. when G is metabelian) the construction yields an endomorphism semigroup, but in the special case where Gis nilpotent (and may therefore, for our present purposes, be considered as a p-group) a group of automorphisms results.

O jisté pologrupě endomorfismů na jednoduše uspořádané množině. II.

O jisté pologrupě endomorfismů na jednoduše uspořádané množině. II.

Bemerkung zu einer Halbgruppe der Endomorphismen auf einer einfach geordneten Menge

Bemerkung zu einer Halbgruppe der Endomorphismen auf einer einfach geordneten Menge

O jisté pologrupě endomorfismů na jednoduše uspořádané množině. I.

O jisté pologrupě endomorfismů na jednoduše uspořádané množině. I.

Semigroup of Endomorphisms of a Locally Compact Group

Semigroup of Endomorphisms of a Locally Compact Group

Semigroup of endomorphisms of a locally compact group

Semigroup of endomorphisms of a locally compact group