On Closed Ideals of βG

For every discrete group G, the Stone-Cech compactification βG has a natural structure of a right topological semigroup. Using the concept of Boolean group ideal on G, we propose a way of constructing closed ideals of the semigroup βG. In particular, we show that, for every infinite Abelian group G of cardinality κ, there are distinct closed ideals in βG.     

Groups in the class semigroups of valuation domains

It is shown that the isomorphy classes of the ideals of a valuation domain form a Clifford semigroup, and the structure of this semigroup is investigated. The group constituents of this Clifford semigroup are exactly the quotients of totally ordered complete abelian groups, modulo dense subgroups. A characterization of these groups is obtained, and some realization results are proved when the skeleton of the totally ordered group is given. The authors are members of GNSAGA of CNR. This research was supported by Ministero dell'Università e della Ricerca Scientifica e Tecnologica, Italy.     

半群的次极大理想与次极小理想

在半群中引入次极大理想和次极小理想的概念，研究了它们的基本性质．证明了次极大理想的存在性，并得到如下定理，半群中每个理想可以分解成一些次极大理想的交，特别地，在满足理想降链条件的半群中，每个理想可以分解成有限个次极大理想的交，对于次极小理想．可以得到对偶的结果．     

阿基米德序半群的链的若干刻画

本文首先引入了一个序半群$S$的准素模糊理想的概念,通过序半群$S$上的一些二元关系以及它的理想的模糊根给出了该序半群是阿基米德序子半群的半格的一些刻画.进一步地借助于序半群$S$的模糊子集对该序半群是阿基米德序子半群的半格进行了刻画.尤其是通过序半群的模糊素根定理证明了序半群$S$是阿基米德序子半群的链当且仅当$S$是阿基米德序子半群的半格且$S$的所有弱完全素模糊理想关于模糊集的包含关系构成链.     

On the Ultrafilter Semigroup of a Topological Group

The ultrafilter semigroup Ult(G) of a topological group G consists of all nonprincipal ultrafilters on G converging to the identity and is a closed subsemigroup in the Stone-Cech compactification βG_d of G as a discrete semigroup. We show that it is consistent with ZFC that for every countable nondiscrete topological group G, Ult(G) can be partitioned into closed right ideals each of which admits a continuous homomorphism onto the Bohr compactification of the integers.     

Prime Ideals of Cancellative Semigroups

Abstract

For a class of prime ideals P of a cancellative semigroup S it is shown that the factors S/P have a structure of a monomial semigroup over a group. Consequences for the semigroup algebras K[S] are discussed.     

Fuzzy半群中的Fuzzy理想

本文先引入Ｆｕｚｚｙ半群中Ｆｕｚｚｙ理想的概念，进而讨论它们的一些代数性质，推广了前人的一些结果。     

Compact operator semigroups applied to dynamical systems

A right chain ordered semigroup is an ordered semigroup whose right ideals form a chain. In this paper we study the ideal theory of right chain ordered semigroups in terms of prime ideals, completely prime ideals and prime segments, extending to these semigroups results on right chain semigroups proved in Ferrero et al. (J Algebra 292:574–584, 2005).     

半群的模糊理想和模糊同余

引入半群上模糊理想、模糊同余的概念。给出它们的一些等价刻划,证明了一个半群上所有模糊同余关系作成一个格。最后,给出模糊理想的积和模糊同余关系的积的概念,讨论了它们的一些性质。     

SEMIGROUPS CHARACTERIZED BY THEIR FUZZY IDEALS

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