Let R be a ring with identity, x be a central element of R which is neither a unit nor azero divisor. S=R/xR is the quotient ring of R and R → R/xR is the natural map.R-Mod(resp. S-Mod) denotes the category of unit...Let R be a ring with identity, x be a central element of R which is neither a unit nor azero divisor. S=R/xR is the quotient ring of R and R → R/xR is the natural map.R-Mod(resp. S-Mod) denotes the category of unital left R-modules(resp. S-modules). In.this paper, relationships betwee torsion theories on R-Mod and torsion theories on S-Mod areinvestigated. Properties of the functor ExtR(N, -) are given. Properties of the localizationfunctor Qσare also investigated.展开更多
文摘Let R be a ring with identity, x be a central element of R which is neither a unit nor azero divisor. S=R/xR is the quotient ring of R and R → R/xR is the natural map.R-Mod(resp. S-Mod) denotes the category of unital left R-modules(resp. S-modules). In.this paper, relationships betwee torsion theories on R-Mod and torsion theories on S-Mod areinvestigated. Properties of the functor ExtR(N, -) are given. Properties of the localizationfunctor Qσare also investigated.
