ALGEBRAIC AND TOPOLOGICAL EQUIVALENCES IN THE STONE-CECH COMPACTIFICATION OF A DISCRETE SEMIGROUP

被引：2

作者：

HINDMAN, N ^{[1
]}

STRAUSS, D ^{[1
]}

机构：

[1] UNIV HULL,SCH MATH,KINGSTON HULL H76 7RX,N HUMBERSIDE,ENGLAND

来源：

TOPOLOGY AND ITS APPLICATIONS | 1995年 / 66卷 / 02期

基金：

美国国家科学基金会;

关键词：

BETA-N; STONE-CECH COMPACTIFICATION; COMPACT RIGHT TOPOLOGICAL SEMIGROUP;

D O I：

10.1016/0166-8641(95)00032-C

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Stone-Cech compactification beta S of a countably infinite discrete commutative semigroup S. We show that, under a certain condition satisfied by all cancellative semigroups S, the minimal right ideals of beta S will belong to 2(c) homeomorphism classes. We also show that the maximal groups in a given minimal left ideal will belong to 2(c) homeomorphism classes. The subsets of PS of the form S + e, where e denotes an idempotent, will also belong to 2(c) homeomorphism classes. All the left ideals of beta N of the form beta N + e, where e denotes a nonminimal idempotent of beta N, will be different as right topological semigroups. If e denotes a nonminimal idempotent of beta Z, e + beta Z will be topologically and algebraically isomorphic to precisely one other principal right ideal of beta Z defined by an idempotent: -e + beta Z. The corresponding statement for left ideals is also valid.

引用

页码：185 / 198

页数：14

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