Vol. 26, No. 3, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Ideal extensions of semigroups

Pierre A. Grillet and Mario Petrich

Vol. 26 (1968), No. 3, 493–508

An ideal extension (here called an extension) of a semigroup S by a semigroup with zero Q is a semigroup V such that S is an ideal of V and the Rees quotient semigroup V∕S is isomorphic to Q. To study the structure of these extensions, special kinds of extensions are introduced, called strict and pure extensions. It is proved that any extension of S is a pure extension of a strict extension of S; also, if Q has no proper nonzero ideals, any extension of S by Q is either strict or pure. Dense extensions, closely related to Ljapin’s “densely embedded ideals”, are special cases of pure extensions. When S is weakly reductive, constructions of strict, pure, and arbitrary extensions of S are given, including descriptions of the ramification function.

Mathematical Subject Classification
Primary: 20.93
Received: 1 April 1966
Published: 1 September 1968
Pierre A. Grillet
Mario Petrich