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Lattice in Pre A*-Algebra

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

Journal: Asian Journal of Algebra
ISSN 1994-540X

Volume: 4;
Issue: 1;
Start page: 1;
Date: 2011;
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Keywords: Pre A-Algebra | irreducible elements | dual atoms | atoms | lattice

ABSTRACT
This study is on algebraic structure of Pre A*-algebra. First we recall partial ordering = on Pre A*-algebra and recall that Pre A*-algebra as a Poset. We recall if A is a Pre A*-algebra then (A, =) is a lattice. We define (for any subset L of a Pre A*-algebra) a lattice (L, ∧, ∨) in a Pre A*-algebra. We define semi lattice, sub lattice and bound elements, bounded lattice, distributive lattice, modular lattice, atoms, dual atoms, irreducible elements in a Pre A*-algebra. We define Pre A*-homomorphism and we prove representation theorem in Pre A*-Algebra also we prove f: A → P (B) is an isomorphism.
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