Displaying similar documents to “On finiteness conditions for Rees matrix semigroups”

Normal cryptogroups with an associate subgroup

Mario Petrich (2013)

Czechoslovak Mathematical Journal

Similarity:

Let S be a semigroup. For a , x ∈ S such that a = a x a , we say that x is an associate of a . A subgroup G of S which contains exactly one associate of each element of S is called an associate subgroup of S . It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup S is a completely regular semigroup whose ℋ -relation is a congruence and S / ℋ is a normal band. Using the representation of S as a strong semilattice of Rees matrix...

Is A - 1 an infinitesimal generator?

Hans Zwart (2007)

Banach Center Publications

Similarity:

In this paper we study the question whether A - 1 is the infinitesimal generator of a bounded C₀-semigroup if A generates a bounded C₀-semigroup. If the semigroup generated by A is analytic and sectorially bounded, then the same holds for the semigroup generated by A - 1 . However, we construct a contraction semigroup with growth bound minus infinity for which A - 1 does not generate a bounded semigroup. Using this example we construct an infinitesimal generator of a bounded semigroup for which its...

On the theory of remediability

Hassan Emamirad (2003)

Banach Center Publications

Similarity:

Suppose G ₁ ( t ) t ≥ 0 and G ₂ ( t ) t ≥ 0 are two families of semigroups on a Banach space X (not necessarily of class C₀) such that for some initial datum u₀, G₁(t)u₀ tends towards an undesirable state u*. After remedying by means of an operator ρ we continue the evolution of the state by applying G₂(t) and after time 2t we retrieve a prosperous state u given by u = G₂(t)ρG₁(t)u₀. Here we are concerned with various properties of the semigroup (t): ρ → G₂(t)ρG₁(t). We define (X) to be the space of remedial operators...

Good and very good magnifiers

Marin Gutan (2000)

Bollettino dell'Unione Matematica Italiana

Similarity:

Un elemento a di un semigruppo S è un elemento accrescitivo sinistro se la traslazione λ a di S , associata all'elemento a , è surgettiva e non è iniettiva (E. S. Ljapin, [13], § 5). Così, per ogni elemento accrescitivo sinistro a , esiste un sottoinsieme proprio M di S tale che la restrizione a M di λ a è biunivoca. Se M è un sottosemigruppo (risp. un ideale destro) di S , l'elemento accrescitivo sinistro a viene detto buono (risp. molto buono) (F. Migliorini [15], [16], [17]). Utilizzando...

On a probabilistic problem on finite semigroups

Attila Nagy, Csaba Tóth (2023)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We deal with the following problem: how does the structure of a finite semigroup S depend on the probability that two elements selected at random from S , with replacement, define the same inner right translation of S . We solve a subcase of this problem. As the main result of the paper, we show how to construct not necessarily finite medial semigroups in which the index of the kernel of the right regular representation equals two.

On semigroups with an infinitesimal operator

Jolanta Olko (2005)

Annales Polonici Mathematici

Similarity:

Let F t : t ≥ 0 be an iteration semigroup of linear continuous set-valued functions. If the semigroup has an infinitesimal operator then it is a uniformly continuous semigroup majorized by an exponential semigroup. Moreover, for sufficiently small t every linear selection of F t is invertible and there exists an exponential semigroup f t : t ≥ 0 of linear continuous selections f t of F t .