Algebra pp 419-442 | Cite as

Tensor Products and Flat Modules

  • Carl Faith
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 190)


Let R be a ring, M a right and N a left R-module. As usual, M × N denotes cartesian product. If G is an abelian group, and g: M× NG is a mapping of sets, then for each yN there is a mapping g y : MG, defined by the formula g y (α) = g (α, y) ∀ αM. Symmetrically, if xM, then g x : NG is defined by the formula g x (b) = g (x, b) ∀bM. A mapping g:M×NG is bilinear in case g y : MG and g x : NG are group homomorphisms ∀ x M,yN. A balanced map g:M×NG is a bilinear map such that
$$g\left( {xr,y} \right) = g\left( {x,ry} \right)$$
x M, yN, rR.


Proal Prool 


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© Springer-Verlag, Berlin · Heidelberg 1973

Authors and Affiliations

  • Carl Faith
    • 1
  1. 1.Rutgers UniversityNew BrunswickUSA

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