We found Gröbner-Shirshov basis for the braid semigroup B n+1. It gives a new algorithm for the solution of the word problem for the braid semigroup and so for the braid group.

A curveX is said to be of type (N, γ) if it is anN–sheeted covering of a curve of genus γ with at least one totally ramified point. A numerical semigroup H is said to be of type (N, γ) if it has γ positive multiples of N in [N, 2Nγ] such that its γ element is 2Nγ and (2γ + 1)N ∈ H. If the genus of X is large enough and N is prime, X is of type (N, γ) if and only if there is a point P ∈ X such t...

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

(sg2) T(0)x = x for all x ∈ C; (sg3) T(s+ t) = T(s)◦T(t) for all s, t ≥ 0; (sg4) for each x ∈ C, the mapping t → T(t)x is continuous. We know that {T(t) : t ≥ 0} has a common fixed point under the assumption that C is weakly compact convex and E has the Opial property; see [3, 4, 5, 6, 8, 10, 12] and other works. Convergence theorems for one-parameter nonexpansive semigroups are proved in [1, 2...

Tameness is a strong property of semigroup pseudovarieties related to the membership problem. Let κ be the signature comprising semigroup multiplication and the omega implicit operation. We prove the κ-tameness of the pseudovarieties N, D, K and LI.

In this paper we show that the congruence classes of A associated to the Burnside semigroup with jAj generators deened by the equation x n = x n+m , for n 4 and m 1, are recognizable. This problem was originally formulated by Brzozowski in 1969 for m = 1 and n 2. Two years ago Aldo de Luca and Stefano Varricchio solved the problem for n 5. A little later, John McCammond extended the problem for...

Anumerical semigroup is a subset ofN containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of algebraic geometry codes, Weierstrass semigroups are crucial for defining bounds on the minimum distance as well as for defining improvements on the dimension of codes...

We associate a discrete-time equation to an exponentially bounded semigroup and we characterize the exponential instability of the semigroup in terms of the complete admissibility of the pair (l∞(N, X), l∞(N, X)). As a consequence, we obtain that in certain conditions a C0-semigroup is exponentially unstable if and only if the pair (Cb(R+, X),Cb(R+, X)) is admissible with respect to an integral...