In this paper A is a commutative noetherian ring, a an ideal of A and the A-modules are
given the a-adic topology. It is a general feeling that completeness is a kind of finiteness …

We assume familiarity with the definitions and basic properties of linearly compact rings and
modules as contained in [6] or [3, Exercises 14 20, pp. 108-111]. In § 1 we show that every …

The notion of secondary representation is in some sense dual to that of primary
decomposition. A module M over the ring A (always assumed to be a com mutative …

Let I be an ideal of a commutative ring R and M an R-module. It is well known that the I-adic
completion functor ΛI defined by ΛI (M)= lim← tM/ItM is an additive exact covariant functor on …

1. Introduction. The present investigation is inspired by a series of papers in the literature,
beginning with Priufer [8], 2 and continuing with Pietrkowski [6; 7], Krull [2; 3], Vilenkin [10; …

Although it is not. true that the section functor r'a with support in the variety of the ideal a
takes a bounded complex of flat modules into a bounded complex of flat modules, a …

Throughout this paper, the word" ring" will mean" commutative,(associative,) Noetherian ring
with a non-zero multiplicative identity". In [9], I discussed the Cousin Complex, C (M), for a …

Let A be a noetherian ring, B an A-algebra of finite type, M a B-module of finite type. If M is a
projective A-module, then Mis A-flat. The converse is not true in general: For instance, let A …

1. Introduction. Therings of this paper are commutative with identity and modules are unital.
The ring of p-adic integers arises quite naturally in abelian group theory as the endomt) …

Let A be a noetherian local ring, and I an ideal of A of dimension one. Our purpose of this
paper is to prove that the category M (A, I) _ cof of cofinite modules is Abelian …