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Proyecciones (Antofagasta)

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Abstract

SRINIVAS, K. V. R  and  ANASUYA, Y. L. PARTIAL ORDERS IN REGULAR SEMIGROUPS. Proyecciones (Antofagasta) [online]. 2010, vol.29, n.3, pp.193-199. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172010000300003.

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 .

Keywords : Locally inverse semigroup; orthodox semigroup; completely regular semigroup; normal band.

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