Vol. 23, No. 1, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
On uniquely divisible semigroups on the two-cell

John A. Hildebrant

Vol. 23 (1967), No. 1, 91–95
Abstract

A topological semigroup S is a Hausdorff space together with a continuous associative multiplication on S. A semigroup S is said to be uniquely divisible if each element of S has unique roots of each positive integral order in S. The present paper concerns uniquely divisible semigroups on the two-cell. The main result of this paper is a statement of equivalent conditions for a commutative uniquely divisible semigroup on the two-cell to be the continuous homomorphic image of the cartesian product of two threads. This result is applied to determine the structure of commutative uniquely divisible semigroups on the two-cell whose idempotent set consists of a zero and an identity.

Mathematical Subject Classification
Primary: 22.05
Milestones
Received: 27 January 1966
Published: 1 October 1967
Authors
John A. Hildebrant