Suppose R and S are local rings and (R,m) → (S,n) is a flat local homomorphism. Given a finitely generated S-module N , we say N is extended (from R) provided there is an R-module M such that S ⊗R M is isomorphic to N as an S-module. If such a module M exists, it is unique up to isomorphism (cf. [EGA, (2.5.8)], and it is necessarily finitely generated. The m-adic completion R → R̂ and the Hensel...

Abstract Free algebras are always free as modules over the base ring in classical algebra. In equivariant algebra, incomplete Tambara functors play role of and Mackey modules. Surprisingly, often fail to be functors. this paper, we determine for all finite groups conditions under which a functor is functor. For solvable groups, show that flat precisely when these hold. Our results imply almost ...

Let $R$ be a commutative ring. An $R$-module $M$ is called semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ $\GV$-torsion for any finitely generated ideal $I$. In this article, we show that the class of modules covering class. Moreover, introduce dimensions $R$-modules and $sr$-$w$-weak global ring $R$. Utilizing these notions, give some homological characterizations $\WQ$-rings $Q_0$-\PvMR s.

For a left and right Noetherian ring $R$, we give some equivalent characterizations for $\_RR$ satisfying the Auslander condition in terms of flat (resp. injective) dimensions minimal injective coresolution resolution) $R$-modules. Furthermore, prove that an artin algebra $R$ condition, is Gorenstein if only subcategory consisting finitely generated modules contravariantly finite. As applicatio...

in this errata, we reconsider and modify two propositions and their corollaries which were written on epi-retractable and co-epi-retractable modules.

This work is devoted to an intrinsic cohomology theory of Koszul-Vinberg algebras and their modules. Our results may be regarded as improvements of the attempt by Albert Nijenhuis in [NA]. The relationships between the cohomology theory developed here and some classical problems are pointed out, e.g. extensions of algebras and modules, and deformation theory. The real Koszul-Vinberg cohomology ...

The configuration management of a sensor network composed of tens or up to thousands of nodes is difficult due to the limit of memory space and energy consumption. This paper presents an approach for dynamic reconfiguration of application modules in sensor networks based on Nano-Qplus. The version information from proposed methods is registered into NVSync (Nano-Qplus Version Synchronization), ...