The ladder construction of Prüfer modules
Let R be a ring (associative, with 1). A non-zero module M is said to be a Prüfer module provided there exists a surjective, locally nilpotent endomorphism with kernel of finite length. The aim of this note is to construct Prüfer modules starting from a pair of module homomorphisms w,v: U0→U1, where w is injective and its cokernel is of finite length. For R=Z the ring of integers, one can construct in this way the ordinary Prüfer groups considered in abelian group theory. Our interest lies in the case that R is an artin algebra.
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Unión Matemática Argentina, Buenos Aires