Flat modules and semiperfect rings
Part of the Mathematics and Its Applications book series (MAIA, volume 449)
Let A be a ring, E A and A M be right and left A-modules, respectively, and let E × M be the cartesian product of these modules. The tensor product E⊖ A M is the Abelian group F/H, where F is the free Z-module with basis indexed by E × M, and H is the subgroup of F generated by all elements of the form
where x, u ∈ E, y, v ∈ M, and a ∈ A.(We write E ⊖ M instead of E ⊖ A M if there is no doubt about A.) The image of (x, y) under a natural map E × M → E ⊖ M is denoted by x ⊖ y.
$$ (x + u,y) - (x,y) - (u,y),(x,y + v) - (x,y) - (x,v),(xa,y) - (x,ay), $$
KeywordsDirect Summand Left Ideal Projective Module Semiprimary Ring Perfect 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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© Springer Science+Business Media Dordrecht 1998