Intrinsic Functions on Semi-Simple Algebras

Abstract

Rinehart (5) has introduced and motivated the study of the class of intrinsic functions on a linear associative algebra , with identity, over the real field R or the complex field C. In this paper we shall consider a semi-simple algebra = ⊕ … ⊕ over R or C with simple components . Let G be the group of all automorphisms or anti-automorphisms of which leave the ground field elementwise invariant, and let H be the subgroup of G such that Ω = (i = 1, 2, … , t) for each Ω in H.