Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 217)
We have seen in Chap. II that to each ring of fractions of a ring A there is associated a notion of torsion for A-modules. The same will be true when we get to consider general rings of quotients of A, but here we will follow a converse course. We start by axiomatizing the concept of torsion, and then to each torsion theory we associate a ring of quotients. This chapter is devoted to a comprehensive study of the general aspects of torsion. The basic result will be that the particular notion of torsion, used in the theory of rings of quotients, can be desribed in three equivalent ways (Gabriel , Maranda ):
by the class of torsion modules,
by the right ideals which serve as annihilators of torsion elements,
by the functor assigning to each module its torsion submodule.
Unable to display preview. Download preview PDF.
© Springer-Verlag Berlin Heidelberg 1975