Endomorphism algebras of torsion modules II

Abstract

This paper is part II of [6]. Let R be a fixed integral domain which has a fixed element O ≠ P ∈ R such that $\mathop \cap \limits_{n \in \omega } {p^n}R = 0.$ If pR is not a maximal ideal and J is an ideal such that p^R ⊑ J ≠ R of the form J = ann_R (x + pⁿR) for some x ∈ R, then we require |R/J| ≥ 4. In this case we say that R is p-representable. There are many p-representable rings, in particular all archimedian valuation domains the ring of the integers ℤ and the ring J_p of p-adic integers. Then R induces on a R-module A the p-adic topology which is generated by pⁿ A, n ∈ ω. Similarly we say that a R-algebra A is p-representable if R is p-representable, and A is as an R-module the completion of a free R-module in this p-adic topology.