Nonholonomic Simple D-modules from Simple Derivations

DERIVATIONS OF TENSOR PRODUCT OF SIMPLE C*-ALGEBRAS

In this paper we study the properties of derivations of A B, where A and B are simple separable C*-algebras, and A B is the C*-completion of A B with respect to a C*-norm Yon A B and we will characterize the derivations of A B in terms of the derivations of A and B

Generalized Derivations on Modules

Arens regularity and derivations of Hilbert modules with the certain product

Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$  is Arens regular. We also study the relationship between derivations of $A$ and $E$.

Gorenstein flat and Gorenstein injective dimensions of simple modules

Let R be a right GF-closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, ...

Applications of epi-retractable modules

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-...