| Title:
|
Generalized $F$-semigroups (English) |
| Author:
|
Giraldes, E. |
| Author:
|
Marques-Smith, P. |
| Author:
|
Mitsch, H. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
203-220 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A semigroup $S$ is called a generalized $F$-semigroup if there exists a group congruence on $S$ such that the identity class contains a greatest element with respect to the natural partial order $\le _{S}$ of $S$. Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup $(S,\cdot ,\le _{S})$ are determined. It is shown that a semigroup $S$ is a generalized $F$-semigroup if and only if $S$ contains an anticone, which is a principal order ideal of $(S,\le _{S})$. Also a characterization by means of the structure of the set of idempotents or by the existence of a particular element in $S$ is given. The generalized $F$-semigroups in the following classes are described: monoids, semigroups with zero, trivially ordered semigroups, regular semigroups, bands, inverse semigroups, Clifford semigroups, inflations of semigroups, and strong semilattices of monoids. (English) |
| Keyword:
|
semigroup |
| Keyword:
|
natural partial order |
| Keyword:
|
group congruence |
| Keyword:
|
anticone |
| Keyword:
|
pivot elements |
| Keyword:
|
partially ordered groups |
| Keyword:
|
principal order ideals |
| MSC:
|
06F15 |
| MSC:
|
20M10 |
| idZBL:
|
Zbl 1111.20050 |
| idMR:
|
MR2148653 |
| DOI:
|
10.21136/MB.2005.134136 |
| . |
| Date available:
|
2009-09-24T22:20:12Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134136 |
| . |
| Reference:
|
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