The property that an ideal whose annihilator is zero contains a regular element is examined from the point of view of constructive mathematics. It is shown that this property holds for nitely presented algebras over discrete elds, and for coherent, Noetherian, strongly discrete rings that contain an in nite eld. Let R be a commutative ring and M an R-module. For any subset I of R, we write AM(I...

In this note we improve and extend duality theorems for crossed products obtained by M. Koppinen (C. Chen) from the case of base fields (Dedekind domains) to the case of an arbitrary Noetherian commutative ground rings under fairly weak conditions. In particular we extend an improved version of the celebrated Blattner-Montgomery duality theorem to the case of arbitrary Noetherian ground rings.

In the derived category of modules over a commutative noetherian ring complex $G$ is said to generate $X$ if latter can be obtained from former by taking summands and finitely many cones. The number cones required in this process generation time $X$. paper we present some local global type results for computing invariant, discuss applications.

Let $C$ be a semidualizing module over commutative Noetherian local ring $R$. In this paper we introduce new class of modules, namely $C$-canonical modules which are generalization canonical modules. It is shown that if the exists then and converse holds under special conditions. Also, characterization Gorenstein rings given via

Let R be a standard graded Noetherian algebra over an Artinian local ring. Motivated by the work of Achilles and Manaresi in intersection theory, we first express the multiplicity of R by means of local j-multiplicities of various hyperplane sections. When applied to a homogeneous inclusion A ⊆ B of standard graded Noetherian algebras over an Artinian local ring, this formula yields the multipl...

Abstract We uncover a connection between the model-theoretic notion of superstability and that noetherian rings pure-semisimple rings. characterize via class left modules with embeddings. Theorem 0.1 For ring R following are equivalent. (1) is noetherian. (2) The R-modules embeddings superstable. (3) every ? ? | + ? 0 , there ? such has uniqueness limit models cardinality ?. (4) Every model in ...

We prove a generalization of the Hochster-Roberts-Boutot-Kawamata Theorem conjectured in [1]: let R → S be a pure homomorphism of equicharacteristic zero Noetherian local rings. If S is regular, then R is pseudo-rational, and if R is moreover Q-Gorenstein, then it is pseudo-log-terminal.

A well known theorem of Shuzo Izumi, strengthened by David Rees, asserts that all the divisorial valuations centered in an analytically irreducible local noetherian ring (R,m) are linearly comparable to each other. This is equivalent to saying that any divisorial valuation ν centered in R is linearly comparable to the m-adic order. In the present paper we generalize this theorem to the case of ...