Birkhoff Centre of a Poset

Autor: Ch. Pragati, R. V. G. Ravi Kumar, G. C. Rao, U. M. Swamy
Rok vydání: 2003
Předmět:
Zdroj: Southeast Asian Bulletin of Mathematics. 26:509-516
ISSN: 0219-175X
0129-2021
DOI: 10.1007/s10012-002-0509-7
Popis: 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.
Databáze: OpenAIRE
Externí odkaz: