Module theory MOC

Balanced product

A balanced product is a certain generalization of a bilinear map for a general module over a (noncommutative) ring . Let be a right -module, be a left -module, and be an abelian group (-module). A map is -balanced iff for all , , module

Together, ^B1 and ^B2 demand biadditivity. Just as bilinear maps are linear maps from the tensor product, -balanced maps are homomorphisms from the Tensor product of modules over a noncommutative ring.

Examples

• Any ring may be regarded as an -Bimodule, in which case the ring multiplication is balanced.

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