

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, semicomplemented, 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: 1222. DOI: 10.3923/aja.2011.12.22 URL: https://scialert.net/abstract/?doi=aja.2011.12.22




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