1. Introduction. R. Keown [5] introduced some new classes of commutative Hilbert algebras which is some sense are generalizations of the algebras studied by W. Ambrose [1]. The essential difference between the works of Keown and Ambrose is that the latter doe not obtain the decomposition of the algebra into orthogonal subspaces each of which is a minimal left ideal. The present authors [4] generalized the work of Ambrose by replacing the underlying Hilbert space structure by a more general space called the semi-inner product space, a concept introduced by G. Lumer [6]. The purpose of this note is to extend some of Keown's results to semi-inner product spaces (henceforth abbreviated to s.i.p, spaces). For example, we show that for any generalized s.i.p, algebra A and for an idempotent e, eAe is a division algebra. For definitions we follow Keown [5] and Husain [2].2. We recall some of the definitions from [4] and [6].A complex (real) vector space X is called a complex (real) s.i.p. space if corresponding to any pair of elements x, y e X, there is defined a complex (real) number [x, y] which satisfies the following properties" ( i ) Ix + y, z] [x, z] + [y, z],[2x, y]--2[x, y] for x, y, z e X, 2 is complex or real, (ii) [x, x]>0 for x0, (iii) I[x, y]l<_ [x, x][y, y]. We put Ilxll=[x, x] and thus X is a normed space. However an s.i.p, space need not satisfy the following properties" (iv) A s.i.p. X space is said to be continuous ifRe {[y, x + 2y]}--.Re {[y, x]} for all real 2-0, and any x, y e X. In a s.i.p, space X, an element x e X is said to be orthogonal to y e X if [y,x]=0. A s.i.p, space is said to be strictly convex if llx+yll=llxll+llyll implies y=2x, >0. An s.i.p, space which is also a Banach algebra is said to be a generalized s.i.p, algebra.