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| Titel: |
A Special Congruence Lattice of a Regular Semigroup |
| Auteur: |
M. Petrich |
| Verschenen in: |
Acta mathematica Universitatis Comenianae |
| Paginering: | Jaargang LXXVI (2007) nr. 2 pagina's 201-214 |
| Jaar: |
2007 |
| Inhoud: |
Let <i>S</i> be a regular semigroup and <b><font face="ARIAL" size="2" style="b">C</font></b> its lattice of congruences. We consider the sublattice <FONT SIZE='3' FACE='Symbol'>L</FONT> of <b><font face="ARIAL" size="2" style="b">C</font></b> generated by <FONT SIZE='3' FACE='Symbol'>s</FONT>-the least group, <FONT SIZE='3' FACE='Symbol'>t</FONT>-the greatest idempotent pure, <FONT SIZE='3' FACE='Symbol'>m</FONT>-the greatest idempotent separating and <FONT SIZE='3' FACE='Symbol'>b</FONT>-the least band congruence on <i>S</i>. To this end, we study the following special cases: (1) any three of these congruences generate a distributive lattice, (2) <FONT SIZE='3' FACE='Symbol'>L</FONT> is distributive, (3) the restriction of the <i>K</i>-relation to <FONT SIZE='3' FACE='Symbol'>L</FONT> is a congruence and (4) a further special case. In each of these instances, we provide several characterizations. Our basic concept is that of a <i>c</i>-triple which represents an abstraction of (<FONT SIZE='3' FACE='Symbol'>L</FONT>; <i>K</i>|<sub><FONT SIZE='3' FACE='Symbol'>L</FONT></sub>, <i>T</i>|<sub><FONT SIZE='3' FACE='Symbol'>L</FONT></sub>) |
| Uitgever: |
Acta Mathematica Universitatis Comenianae, Institute of Applied Mathematics (provided by DOAJ) |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 8 van 63 gevonden artikelen
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