Proyecciones Journal of Mathematics
Vol. 29, N° 3, pp. 193-199, December 2010.
Universidad Católica del Norte
Antofagasta - Chile


PARTIAL ORDERS IN REGULAR SEMIGROUPS


K. V. R. Srinivas¹
Y. L. Anasuya²

¹Regency Institute Of Technology, India
²Andhra University, India


Correspondencia a:

Abstract

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 .

Key Words : Locally inverse semigroup, orthodox semigroup, completely regular semigroup, normal band.

AMS Subject Classification No. :20M18.

References

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K. V. R. Srinivas
Regency institute of technology,
YANAM - 533464
Near Kakinada
e-mail : srinivas_kandarpa06@yahoo.co.in


Y. L. Anasuya
Department of Mathematics
Andhra University
Visakhapatnam
INDIA
e-mail : anasuyapamarthy@gmail.com

Received : April 2009. Accepted : September 2010