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Pre A*-Algebra as a Semilattice

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Author(s): Y. Praroopa | J. Venkateswara Rao

Journal: Asian Journal of Algebra
ISSN 1994-540x

Volume: 4;
Issue: 1;
Start page: 12;
Date: 2011;
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Keywords: Pre A-algebra | complemented semilattice | semilattice

ABSTRACT
This paper is a study on algebraic structure of Pre A*-algebra. First we define partial ordering on Pre A*-algebra. We prove if A is a Pre A*-algebra then (A, =) is a poset. We define a semilattice on Pre A*-algebra. We prove Pre A*-algebra as a semilattice. Next we prove some theorems on semilattice over a Pre A*-algebra. We define distributive and modular semilattices on Pre A*-algebra We define complement, relative complement of an element in Pre A*-algebra. We define complemented semilattice, relatively complemented semilattices in Pre A*-algebra. We give some examples of these semilattices in Pre A*-algebra. We define weakly complemented, semi-complemented, uniquely complemented semilattices in Pre A*-algebra. We prove some theorems on these semilattices in Pre A*-algebra.
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