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Asian Journal of Algebra
  Year: 2011 | Volume: 4 | Issue: 1 | Page No.: 12-22
DOI: 10.3923/aja.2011.12.22
 
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Pre A*-Algebra as a Semilattice

Y. Praroopa and J. Venkateswara Rao

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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How to cite this article:

Y. Praroopa and J. Venkateswara Rao, 2011. Pre A*-Algebra as a Semilattice. Asian Journal of Algebra, 4: 12-22.

DOI: 10.3923/aja.2011.12.22

URL: https://scialert.net/abstract/?doi=aja.2011.12.22

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