It is proved that a ring A right or left Noetherian, distributive, centrally essential if and only [Formula: see text], where each of the rings text] either commutative Dedekind domain Artinian, uniserial ring.

We study skew inverse power series extensions R[[y−1; τ, δ]], where R is a noetherian ring equipped with an automorphism τ and a τ -derivation δ. We find that these extensions share many of the well known features of commutative power series rings. As an application of our analysis, we see that the iterated skew inverse power series rings corresponding to nth Weyl algebras are complete, local, ...

This a first step to develop a theory of smooth, étale and unramified morphisms between noetherian formal schemes. Our main tool is the complete module of differentials, that is a coherent sheaf whenever the map of formal schemes is of pseudo finite type. Among our results we show that these infinitesimal properties of a map of usual schemes carry over into the completion with respect to suitab...

Recall that a regular local ring is a noetherian local ring with dimension equal to dimkm/m. A regular local ring of dimension one is precisely a discrete valuation ring. If V is a nosingular variety then t(V ) is a scheme with all local rings regular, so t(V ) is clearly regular in codimension one. In this section we will consider schemes satisfying the following condition: (∗) X is a noetheri...

Suppose S is an affine, noetherian scheme, X is a separated, noetherian S-scheme, E is a coherent OX -bimodule and I ⊂ T (E) is a graded ideal. We study the geometry of the functor Γn of flat families of truncated B = T (E)/I-point modules of length n + 1. We then use the results of our study to show that the point modules over B are parameterized by the closed points of P X2(E). When X = P , w...

Let R be a commutative noetherian local ring, and let X be a resolving subcategory of the category of finitely generated R-modules. In this paper, we study modules in X by relating them to modules in X which are free on the punctured spectrum of R. We do this by investigating nonfree loci and establishing an analogue of the notion of a level in a triangulated category which has been introduced ...

All rings considered are associative with identity and all occurring modules are unital right modules. We denote by Mod R the category of all R-modules. The spectrum of a ring R is known to be the “set” of isomorphism classes of indecomposable injective right R-modules. When R is right-Noetherian the spectrum describes all injective Rmodules, since each injective module is a direct sum of indec...

Let D be a domain with quotient field K and A a D-algebra. A polynomial with coefficients in K that maps every element of A to an element of A is called integer-valued on A. For commutative A we also consider integer-valued polynomials in several variables. For an arbitrary domain D and I an arbitrary ideal of D we show I -adic continuity of integer-valued polynomials on A. For Noetherian one-d...

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

Motivated by their impact on homological algebra, the change of rings results have been the subject of several interesting works in Gorenstein homological algebra over Noetherian rings. In this paper, we investigate the change of rings theorems for the Gorenstein dimensions over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we extend the well-known first, sec...