Birkhoff Centre of a Poset |
| |
Authors: | U. M. Swamy G. C. Rao R. V. G. Ravi Kumar Ch. Pragati |
| |
Affiliation: | (1) Department of Mathematics, Andhra University, Visakhapatnam, 530 003, India |
| |
Abstract: | In this paper, it is proved that the Boolean centre of a semigroup S with sufficiently many commuting idempotents is isomorphic to the inverse limit of the directed family of Birkhoff centres (or Boolean centres) of a class of bounded semigroups. The Birkhoff centre is defined for any poset and proved that it is a relatively complemented distributive lattice whenever it is nonempty. It is observed that for a semilattice S, the Birkhoff centres as a semigroup and as a poset coincide. Also it is observed that for a Lattice (L, , ), the Birkhoff centres of the semilattices (L, ) and (L, ) coincide with the Birkhoff centre of L. Finally it is proved that for a lattice (L, , ), the Boolean centres of the semilattices (L, ) and (L, ) coincide with the Boolean centre of L.AMS Subject classification (1991): 06A12, 20M15 |
| |
Keywords: | Birkhoff centres of a poset and semigroup Direct factor Balanced direct factor Boolean centre Inverse limit |
本文献已被 SpringerLink 等数据库收录! |
|