Anti-uniform semilattices
- 17 April 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 1 (2) , 263-268
- https://doi.org/10.1017/s0004972700041502
Abstract
An inverse semigroup which is a union of groups is called Cliffordian. A semilattice E is called universally Cliffordian if every inverse semigroup having E as semilattice of idempotents is Cliffordian. It is shown that E is universally Cliffordian if and only if it is anti-uniform, that is, if and only if no two distinct principal ideals of E are isomorphic.A semilattice E satisfying the minimum condition is anti-uniform if and only if it is a well-ordered chain. Examples are given of anti-uniform semilattices of more complicated types.Keywords
This publication has 1 reference indexed in Scilit:
- On the Arithmetic of Order TypesTransactions of the American Mathematical Society, 1959