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 non-normal affine semigroup rings are also of finite F-representation type, whereas normal affine semi-computations are of F-approximation type.
Abstract: It is known that normal affine semigroup rings are of finite F-representation type. In this paper, we prove that non-normal affine semigroup rings are also of finite F-representation type.
3 citations
TL;DR: In this paper, the existence problem for bounded solutions of linear differential inclusions is studied for distribution semigroups with a singularity at zero and their generators, and a relationship between this semigroup and a degenerate semigroup of linear operators on the open right half line is established.
Abstract: We study distribution semigroups with a singularity at zero and their generators, and establish a relationship between this semigroup and a degenerate semigroup of linear operators on the open right half-line. The study makes an intensive use of spectral theory of linear relations. Applications to the existence problem for bounded solutions of linear differential inclusions are obtained.
3 citations
01 Jan 1975
TL;DR: In this paper, it was shown that any maximal cancellative subsemigroup T of a commutative, idempotent-free, archimedean semigroup S must be a mild ideal of S. It is also shown that if T is mild ideal, then every cancellative congruence of T has a unique extension to a cancellative CONGUE of S, and that T is also a semigroup that can be seen as an extension to S.
Abstract: A subsemigroup T of a commutative semigroup S is called a mild ideal if for any a E S, aT n T / 0. It is shown here that any maximal cancellative subsemigroup T of a commutative, idempotentfree, archimedean semigroup S must be a mild ideal of S. Maximal cancellative subsemigroups exist in abundance due to Zorn's lemma. It is also shown that if T is mild ideal of a commutative semigroup S, then every cancellative congruence of T has a unique extension to a cancellative congruence of S. 1. Maximal cancellative subsemigroups. Let S be a commutative archimedean semigroup with no idempotents. Let A be a cancellative subsemigroup of S. By the Hausdorff maximal principle (Zorn's lemma), there will exist a maximal 1 cancellative subsemigroup T such that A C T. In particular if a E 5, then the cyclic semigroup (a) is cancellative, and hence there exists a maximal cancellative subsemigroup of S containing a. In what follows, Z + denotes the set of positive integers. We start with Lemma 1. 1. Let S be a commutative, archimedean, idempotent-free semigroup and let T be a maximal cancellative subsemigroup of S. Then for any a E S\T, there exists i E Z+ and t , t2 E T1, u E T, such that ait u = t2u but a' t 4 t2. Proof. We use, without further comment, a result of Tamura (see [21 or [31) that for any a, b E 5, ab 4 b. Now let a E S\T. By maximality of T, the semigroup generated by a and T is not cancellative. So there exist nonnegative integers j, k and t1, t2 E T1 x E 5, such that a't1 7 a t2; 1 t x= a t2x. If j= k, then t a x = t2a x. Since S is archimedean, Received by the editors November 16, 1973. AMS (MOS) subject classifications (1970). Primary 20M10.
3 citations
TL;DR: In this article, the authors studied Noetherian local subrings of, such that, and with nonzero conductor, i.e., rings of the form, where are polynomials (or power series).
Abstract: We study Noetherian local subrings of , such that , and with nonzero conductor , i.e., rings of the form , where are polynomials (or power series). For every such ring, is a numerical semigroup. Let be a numerical semigroup. Then is called a semigroup ring if for some . is called monomial if each ring with value semigroup is a semigroup ring. We discuss this and some related concepts.
3 citations
TL;DR: In this paper, the authors give counterexamples for the open problem of whether weak amenability of a semigroup algebra l 1(S) implies complete regularity of the semigroup S. The counterexpansion of the problem is shown to be 0-cancellative.
Abstract: In this paper we give counterexamples for the open problem, posed by Blackmore (Semigroup Forum 55:359–377, 1987) of whether weak amenability of a semigroup algebra l1(S) implies complete regularity of the semigroup S. We present a neat set of conditions on a commutative semigroup (involving concepts well known to those working with semigroups, e.g. the counterexamples are nil and 0-cancellative) which ensure that S is irregular (in fact, has no nontrivial regular subsemigroup), but l1(S) is weakly amenable. Examples are then given.
3 citations