ﻻ يوجد ملخص باللغة العربية
Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors with supports in arbitrary subsets of Spec R, which is a natural generalization of right derived functors of section functors with supports in specialization-closed subsets. We prove that the local duality theorem and the vanishing theorem of Grothendieck type hold for colocalization functors.
We describe new classes of noetherian local rings $R$ whose finitely generated modules $M$ have the property that $Tor_i^R(M,M)=0$ for $igg 0$ implies that $M$ has finite projective dimension, or $Ext^i_R(M,M)=0$ for $igg 0$ implies that $M$ has fini
We develop new methods to study $mathfrak{m}$-adic stability in an arbitrary Noetherian local ring. These techniques are used to prove results about the behavior of Hilbert-Samuel and Hilbert-Kunz multiplicities under fine $mathfrak{m}$-adic perturbations.
Let R be a commutative ring with identity. We investigate some ring-theoretic properties of weakly Laskerian R-modules. Our results indicate that weakly Laskerian rings behave as Noetherian ones in many respects. However, we provide some examples to
It is proven that each indecomposable injective module over a valuation domain $R$ is polyserial if and only if each maximal immediate extension $widehat{R}$ of $R$ is of finite rank over the completion $widetilde{R}$ of $R$ in the $R$-topology. In t
Let $mathcal{I}(R)$ be the set of all ideals of a ring $R$, $delta$ be an expansion function of $mathcal{I}(R)$. In this paper, the $delta$-$J$-ideal of a commutative ring is defined, that is, if $a, bin R$ and $abin Iin mathcal{I}(R)$, then $ain J(R