A note on compact semirings which are multiplicative semilattices

P. H. Karvellas

Vol. 55 (1974), No. 1, 195–205

DOI: 10.2140/pjm.1974.55.195

Abstract

The topic of this note is the structure of a topological semiring in which a semilattice (commutative, idempotent and associative) multiplication, with identity and connected upper sets, has been postulated. Assuming the topology to be compact, additions compatible with the multiplication can be characterized for certain canonical subsets of the semiring. In particular instances the characterization of addition can be extended to the entire semiring itself.

Mathematical Subject Classification 2000

Primary: 22A99

Milestones

Received: 28 March 1973

Revised: 24 July 1973

Published: 1 November 1974