On finiteness conditions for Rees matrix semigroups

Hayrullah Ayik

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

Normal cryptogroups with an associate subgroup

Mario Petrich (2013)

Czechoslovak Mathematical Journal

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Let $S$ be a semigroup. For $a, x \in S$ 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

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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

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Suppose ${G ₁ (t)}_{t \geq 0}$ and ${G ₂ (t)}_{t \geq 0}$ 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

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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...

Linear modulus of a multidimensional semigroup of $L_{1}$ -contractions and a differentiation theorem

Dogan Çömez (1989)

Colloquium Mathematicae

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On the probability that two elements of a finite semigroup have the same right matrix

Attila Nagy, Csaba Tóth (2022)

Commentationes Mathematicae Universitatis Carolinae

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We study the probability that two elements which are selected at random with replacement from a finite semigroup $S$ have the same right matrix.

On semigroups with an infinitesimal operator

Jolanta Olko (2005)

Annales Polonici Mathematici

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Let $F^{t} : t \geq 0$ 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 $f^{t} : t \geq 0$ of linear continuous selections $f^{t}$ of $F^{t}$ .

On some free semigroups, generated by matrices

Piotr Słanina (2015)

Czechoslovak Mathematical Journal

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Let $A = [\begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}], B_{λ} = [\begin{matrix} 1 & 0 \\ λ & 1 \end{matrix}] .$ We call a complex number $λ$ “semigroup free“ if the semigroup generated by $A$ and $B_{λ}$ is free and “free” if the group generated by $A$ and $B_{λ}$ is free. First families of semigroup free $λ$ ’s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free $λ$ ’s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common...

On the K-theory of the $C^{*}$ -algebra generated by the left regular representation of an Ore semigroup

Joachim Cuntz, Siegfried Echterhoff, Xin Li (2015)

Journal of the European Mathematical Society

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We compute the $K$ -theory of $C^{*}$ -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the $K$ -theory of these semigroup $C^{*}$ -algebras in terms of the $K$ -theory for the reduced group $C^{*}$ -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.

Locally adequate semigroup algebras

Yingdan Ji, Yanfeng Luo (2016)

Open Mathematics

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We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant [...] 0-J* $0 - 𝒥 *$ -simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the [...] ℛ* $ℛ *$ -classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we...