Baer-invariants of algebras

Abstract

Explicitly this paper deals with functors of the category GA of associative algebras-not necessarily with identity-over a commutative ring A with identity. The contents of the first part remain valid however in a much more general situation. We have formulated the theory of Baer-invariants in 1-3 in the language of A-algebras, in order to exhibit their significance in a concrete category and also in order to preserve the continuity with the later sections. The translations into abstract terms does not present any difficulty. It is in particular clear that the definitions and results of 1-3 apply equally well to any variety of groups with multiple operators in the sense of P. J. Higgins (cf. [3]).