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.     

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).     

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。     

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

ＳＥＭＩＧＲＯＵＰＳＣＨＡＲＡＣＴＥＲＩＺＥＤＢＹＴＨＥＩＲＦＵＺＺＹＩＤＥＡＬＳＪ．ＡｈｓａｎａｎｄＫ．Ｓａｉｆｕｌｌａｈ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅｓＫｉｎｇＦａｈｄＵｎｉｖｅｒｓｉｔｙｏｆＰｅｔｒｏｌｅｕｍａ...     

序半群素模糊理想的刻画

研究序半群S的素模糊理想，通过S的模糊左（右）理想和序模糊点给出了S的素模糊理想的等价刻画。     

On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations

We characterize the maximal regular subsemigroups of the ideals of the semigroup of all order-preserving transformations as well as of the semigroup of all order-preserving or order-reversing transformations on a finite ordered set.     

Fuzzy半群中的极小Fuzzy理想

本文先给出Ｆｕｚｙ半群中极小Ｆｕｚｙ理想的一些代数性质,进而利用极小Ｆｕｚｙ理想刻划Ｆｕｚｚｙ单半群的一些代数性质     

阿基米德序半群的链(英文)

本文通过一个序半群S上的一些二元关系以及它的理想(右理想,双理想)的根集分别给出了该序半群是阿基米德(右阿基米德,t-阿基米德)序子半群的链的刻画.进一步证明了准素序半群是阿基米德序半群的链.最后,通过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的所有素理想关于集合的包含关系构成链.     

Well-posedness and stability of nonautonomous past systems with unbounded operators in the delay term

Semigroup Forum - We define a semigroup S to be right ideal Howson if the intersection of any two finitely generated right ideals, or, equivalently, any two principal right ideals, is again...     

Sur les ideaux des demi-groupes nilpotents

In this paper, we establish several properties of the lattice of ideals of a nilpotent semigroup. In particular, we characterize the finite nilpotent semigroups by the length of this lattice, and we generalize a theorem of T. Tamura and M. Yamada [5], concerning the ideal extension of a nilpotent semigroup by a null semigroup.      

真理想为Archimedean子半群的偏序半群

根据真理想情况给出了偏序半群的一种分类，研究了真理想为Archimedean子半群的偏序半群的特征．     

粗糙子群和粗糙子环

文[1]研究了半群中的理想,首次提出了粗半群和粗理想的概念.本文继续研究了群中的粗糙子群和粗正规子群.同时,在环中引入了粗子环的概念.最后,研究了粗糙集的同态问题.