Endomorphism rings of reduced complete torsion-free modules over complete discrete valuation rings

A Classification of Modules over Complete Discrete Valuation Rings

Endomorphism Rings of Modules over Prime Rings

Endomorphism rings of modules appear as the center of a ring, as the fix ring of a ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain ∗-prime modules have a prime endomorphism ring. Several conditions are presented that guarantee the primeness of the endomorphism ring. The contours of a possible example of a ∗-prime module who...

On Ramified Complete Discrete Valuation Rings

Complete fields and valuation rings

In order to make further progress in our investigation of finite extensions L/K of the fraction field K of a Dedekind domain A, and in particular, to determine the primes p of K that ramify in L, we introduce a new tool that allows us to “localize” fields. We have seen how useful it can be to localize the ring A at a prime ideal p: this yields a discrete valuation ring Ap, a principal ideal dom...

Endomorphism Rings of Protective Modules

The object of this paper is to study the relationship between certain projective modules and their endomorphism rings. Specifically, the basic problem is to describe the projective modules whose endomorphism rings are (von Neumann) regular, local semiperfect, or left perfect. Call a projective module regular if every cyclic submodule is a direct summand. Thus a ring is a regular module if it is...