Trends in Applied Sciences Research 1819-3579 2151-7908 Science International 10.3923/tasr.2011.108.120 Satyanarayana A. Rao J. Venkateswara Suryakumar U. 2 2011 6 2 In this study we formulate the definitions of an ideal, prime ideal, maximal ideal of Pre A*-algebra A and discuss certain examples. We prove important fundamental properties of Ideals. In particular we extend to prove that every ideal I of a Pre A*-algebra A is the intersection of all prime ideals of A containing I. We also show that every maximal ideal is necessarily prime, while the converse is true for special cases only.

]]> 1 Birkhoff, G., 1948 Lattice Theory. 2 Guzman, F. and C.C. Squier, 1990 Algebra Univ., 27 88 110 3 Jocobson, N., 1994 Basic Algebra. Vol. 1, 4 Koteswara Rao, P., 1994 A*-Algebras and if-then-else structures. 1994 5 Koteswara Rao, P. and J. Venkateswara Rao, 2003 J. Pure Math., 20 33 38 6 Koteswara Rao, P. and J. Venkateswara Rao, 2004 Southeast Asian Bull. Math., 28 1099 1119 7 Koteswara Rao, P. and J. Venkateswara Rao, 2005 A Cayley theorem for A-Algebras. 2005 8 Koteswara Rao, P. and J. Venkateswara Rao, 2008 Int. J. Comput. Math. Appl., 2 103 108 9 Manes, E.G., 1989 The equational theory of disjoint alternatives. 1989 10 Manes, E.G., 1993 Algebra Universalis, 30 373 394 11 Rao, J.V., 2000 On A*-algebras. 2000 12 Venkateswara Rao, J. and K. Srinivasa Rao, 2009 Afr. J. Math. Comput. Sci. Res., 2 73 80 13 Venkateswara Rao, J., K. Srinivasa Rao, T. Nageswara Rao and R.V.N. Srinivasa Rao, 2009 Int. J. Syst. Cybernet. Inform., 1 14 19