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An alternative perspective on flatness of modules
(World Scıentıfıc Publ Co Pte Ltd, 2016)
Given modules M-R and A(R), M-R is said to be absolutely A(R)-pure if A circle times M -> A circle times B is a monomorphism for every extension B-R of M-R. For a module AR, the absolutely pure domain of A(R) is defined ...
Small supplements, weak supplements and proper classes
(Hacettepe Unıv, Fac Scı, 2016)
Let SS denote the class of short exact sequences E :0 -> A (f) under right arrow B -> C -> 0 of R-modules and R-module homomorphisms such that f(A) has a small supplement in B i.e. there exists a submodule K of M such that ...
Neat-flat Modules
(Taylor & Francıs Inc, 2016)
Let R be a ring. A right R- module M is said to be neat- flat if the kernel of any epimorphism Y -> M is neat in Y, i. e., the induced map Hom(S, Y) -> Hom(S, M) is surjective for any simple right R-module S. Neat-flat ...