Maximal Groups in Stone-Cech Compactifications: Discrete Semigroups - Softcover

Legette, Lakeshia

Softcover

ISBN 10: 3639102002 ISBN 13: 9783639102000

Publisher: VDM Verlag, 2009

Synopsis

I take the points of the Stone-Cech Compactification of a semigroup T to be the set of all ultrafilters on T, the principal ultrafilters being identified with the points of T. There is a natural extension of the operation of T to its Stone- Cech Compactification, making it a compact right topological semigroup. A subset V of a semigroup T is called a left ideal if it is nonempty and TV is a subset of V. It is called a right ideal if it is nonempty and VT is a subset of V. The intersection of any minimal left ideal and minimal right ideal is a group, called a maximal group. However, the structure of these groups is not guaranteed to be an interesting one. For some semigroups, this group may be relatively large and for others it may be small. An important class of semigroups is the free semigroups. When A is a nonempty set, the free semigroup on the alphabet A is the set of all words on A. In this book, it is shown that it is consistent that there exists a special type of ultrafilter for which the maximal group is a single element.

About this title

About the Author

Lakeshia R. Legette, PhD: Assistant Professor in the Department of Natural Sciences & Mathematics at Johnson C. Smith University in Charlotte, NC; Studied Mathematics at Howard University in Washington, DC under the advisement of Dr. Neil Hindman.

Edition details

• Publisher: VDM Verlag
• Publication date: 2009
• ISBN 10: 3639102002
• ISBN 13: 9783639102000
• Binding: Paperback
• Language: English
• Number of pages: 64