PARTIAL ORDERS IN REGULAR SEMIGROUPS
First we have obtained equivalent conditions for a regular semigroup and is equivalent to N = N1 It is observed that every regular semigroup is weakly separative and C ? S and on a completely regular semigroup S ? N and S is partial order . It is also obtained that a band (S, .) is normal iff C = N...
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| Autores principales: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2010
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000300003 |
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| Sumario: | First we have obtained equivalent conditions for a regular semigroup and is equivalent to N = N1 It is observed that every regular semigroup is weakly separative and C ? S and on a completely regular semigroup S ? N and S is partial order . It is also obtained that a band (S, .) is normal iff C = N . It is also observed that on a completely regular semigroup (S, .), C = S = N iff (S, .) is locally inverse semigroup and the restriction of C to E(S) is the usual partial order on E(S). Finally it is obtained that, if (S, .) is a normal band of groups then C = S = N . |
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