Cancellative semigroup

About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.

The modulus of matrix semigroups

Abstract: We treat a result concerning the generator of the modulus semigroup of a strongly continuous semigroup acting on the product of Banach lattices with order continuous norm.

A Note on Numerical Semigroups

Abstract: This correspondence is a short extension to the previous article Bras-Amoroacutes, 2004. In that work, some results were given on one-point codes related to numerical semigroups. One of the crucial concepts in the discussion was the so-called nu-sequence of a semigroup. This sequence has been used in the literature to derive bounds on the minimum distance as well as for defining improvements on the dimension of existing codes. It was proven in that work that the nu-sequence of a semigroup uniquely determines it. Here this result is extended to another object related to a semigroup, the oplus operation. This operation has also been important in the literature for defining other classes of improved codes. It is also proven here that, although the infinite set of values in the nu-sequence (resp. the oplus values) uniquely determines the associated semigroup, no finite part of it can determine it, because it is shared by infinitely many semigroups. In that reference the proof of the fact that the nu-sequence of a numerical semigroup uniquely determines it is constructive. The result here presented shows that, however, that construction can not be performed as an algorithm with finite input

Levi’s Commutator Theorems for Cancellative Semigroups

Abstract: For every semigroup of finite exponent whose chains of idempotents are uniformly bounded we construct an identity which holds on this semigroup but does not hold on the variety of all idempotent semigroups. This shows that the variety of all idempotent semigroups E is not contained in any finitely generated variety of semigroups. Since E is locally finite and each proper subvariety of E is finitely generated [1, 3, 4], the variety of all idempotent semigroups is a minimal example of an inherently non-finitely generated variety.

Embedding Semigroups into Idempotent Generated Ones

Abstract: We present a concrete model of the embedding due to Pastijn and Yan of a semigroup S into an idempotent generated semigroup now in terms of a Rees matrix semigroup over S1. The paper starts with a comparison of the two embeddings. Studying the properties of this embedding, we prove that it is functorial. We show that a number of usual semigroup properties is preserved by this embedding, such as periodicity, finiteness, the cryptic property, regularity, complete semisimplicity and various local properties, but complete regularity is not one of them.

Nonlinear monotone semigroups and viscosity solutions

Abstract: In a celebrated paper motivated by applications to image analysis, L. Alvarez, F. Guichard, P.-L. Lions and J.-M. Morel showed that any monotone semigroup defined on the space of bounded uniformly continuous functions, which satisfies suitable regularity and locality assumptions is in fact a semigroup associated to a fully nonlinear, possibly degenerate, second-order parabolic partial differential equation. In this paper, we extend this result by weakening the assumptions required on the semigroup to obtain such a result and also by treating the case where the semigroup is defined on a general space of continuous functions like, for example, a space of continuous functions with a prescribed growth at infinity. These extensions rely on a completely different proof using in a more central way the monotonicity of the semigroup and viscosity solutions methods. Then we study the consequences on the partial differential equation of various additional assumptions on the semigroup. Finally we briefly present the adaptation of our proof to the case of two-parameters families.