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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)

Abstract

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.

Keywords

Abelian Group Tensor Product Commutative Ring Left Ideal Noetherian Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag, Berlin · Heidelberg 1973

Authors and Affiliations

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

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