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Asian Journal of Algebra
  Year: 2011 | Volume: 4 | Issue: 1 | Page No.: 1-11
DOI: 10.3923/aja.2011.1.11
 
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Lattice in Pre A*-Algebra

Y. Praroopa and J.V. Rao

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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How to cite this article:

Y. Praroopa and J.V. Rao, 2011. Lattice in Pre A*-Algebra. Asian Journal of Algebra, 4: 1-11.

DOI: 10.3923/aja.2011.1.11

URL: https://scialert.net/abstract/?doi=aja.2011.1.11

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