Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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TL;DR: In this paper, it was shown that such a nice explicit representation of the Dirichlet-to-Neumann semigroup is not possible for any domain except Euclidean balls, and they presented a natural and probably the simplest numerical scheme to calculate this semigroup in full generality by using Chernoff's theorem.
Abstract: In his book (Functional Analysis, Wiley, New York, 2002), P. Lax constructs an explicit representation of the Dirichlet-to-Neumann semigroup, when the matrix of electrical conductivity is the identity matrix and the domain of the problem in question is the unit ball in ℝn. We investigate some representations of Dirichlet-to-Neumann semigroup for a bounded domain. We show that such a nice explicit representation as in Lax book, is not possible for any domain except Euclidean balls. It is interesting that the treatment in dimension 2 is completely different than other dimensions. Finally, we present a natural and probably the simplest numerical scheme to calculate this semigroup in full generality by using Chernoff’s theorem.
7 citations
TL;DR: In this article, Miyadera et al. established a theorem on convergence of (A)-semigroups and, as its simple consequences, theorems on convergence for (0, A) and (1, A)-Semigroups on a Banach space.
7 citations
TL;DR: In this paper, the structure of a commutative multiplicative semigroup and its corresponding class semigroup are determined by means of its partial Ponizovski factors, in terms of the different and conductor of their endomorphism rings.
7 citations
01 Oct 1988
TL;DR: In this article, Nambooripad's generalization of Munn's results to regular semigroups has been studied, and it has been shown that any regular semigroup is a coextension of a fundamental inverse semigroup which possesses the same set of idempotents.
Abstract: In any extension theory for semigroups one must determine the basic building blocksand then discover how they fit together to create more complicated semigroups. Forexample, in group theory the basic building blocks are simple groups. In semigrouptheory however there are several natural choices. One that has received considerableattention, particularly since the seminal work on inverse semigroups by Munn ([14,15]), is the notion of a fundamental semigroup. A semigrou fundamentalp i isf calle it dcannot be "shrunk" homomorphically without collapsing some of its idempotents (seebelow for a precise definition).For example, Munn showed how all fundamental inverse semigroups can beconstructed from semilattices, and proved that any inverse semigroup is a coextension ofa fundamental inverse semigroup which possesses the same semilattice of idempotents.(A semigroup S is called a coextension of a semigroup T if T is a homomorphic imageof S.) This work has been generalized by several authors to wider classes of semigroups([12, 1, 11, 16, 4]).The idempotents of an arbitrary semigroup form a biordered set. (Regular biorderedsets form the basis for Nambooripad's generalization of Munn's results to regularsemigroups). One might ask whether an arbitrary semigroup is a coextension of afundamental semigroup possessing the same biordered set of idempotents. The followingexample shows the answer is negative.Let S = (e,f\e
7 citations
7 citations