RD-flatness and RD-injectivity
Francois Couchot
Abstract
It is proved that every commutative ring whose RD-injective modules are Σ-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively the RD-relativization of flat modules and fp-injective modules. It is also shown that a commutative ring is perfect if and only if each RD-flat module is RD-projective.
Create a lesson
Related papers
Directed partial orders on the complex number field
Wenyi Wang, Ruisong Yuan, Yuehui Zhang et al.
Polynomial identities, central polynomials and cocharacters of M2(F) with G-graded involution
Rafael Bezerra dos Santos, Lucas Reis
Polynomial identities, central polynomials and cocharacters of M2(F) with transpose superinvolution
Rafael Bezerra dos Santos, Lucas Reis
Range-compatible homomorphisms on Hermitian matrices
Clément de Seguins Pazzis
Transposed Triple Products and Pro-Symmetric Rings in -Rings
Huaxi Chen, Long Wang, Honglin Zou
On -Reversible and Generalized -Reversible Rings
Huaxi Chen, Long Wang, Honglin Zou