ABSTRACT
A-balanced mapping Let M be a right module over the ring A, and let N be a left module over the same ringA. A mapping φ fromM×N to an Abelian group G is said to be A-balanced if φ(x, ·) is a group homomorphism from N to G for each x ∈ M , if φ(·, y) is a group homomorphism from M to G for each y ∈ N , and if
φ(xa, y) = φ(x, ay) holds for all x ∈ M , y ∈ N , and a ∈ A. A-B-bimodule An Abelian group G that is a left module over the ring A and a right module over the ring B and satisfies the associative law (ax)b = a(xb) for all a ∈ A, b ∈ B, and all x ∈ G. Abelian cohomology The usual cohomology with coefficients in an Abelian group; used if the context requires one to distinguish between the usual cohomology and the more exotic nonAbelian cohomology. See cohomology.
