Abstract
The construction by Hall of a fundamental orthodox semigroup W-B from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup S-B that plays the role of W-B for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider are weakly B-abundant and satisfy the congruence condition (C). Any orthodox semigroup S with E(S)=B lies in our class. On the other hand, if a semigroup S lies in our class, then S is Ehresmann if and only if B is a semilattice.
The Hall semigroup W-B is a subsemigroup of S-B , as are the (weakly) idempotent connected semigroups V-B and U-B . We show how the structure of S-B can be used to extract information relating to arbitrary weakly B-abundant semigroups with (C).
| Original language | English |
|---|---|
| Pages (from-to) | 279-299 |
| Number of pages | 21 |
| Journal | Semigroup forum |
| Volume | 77 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Oct 2008 |
Keywords
- Hall semigroup
- band
- fundamental
- weakly abundant