Assume that A and B are rings with identity and that M and N are (B,A) and (A,B) bimodules respectively. We say that AN (respt. MA) is partially flat (respt. projective) with respect to a subcategory C(A) of Mod-A (the category of all unital right A-modules), if the tensor functor, -⊗AN (respt. the hom functor HomA(M,-)) is exact on C(A). For example, a flat or a projective module is partially flat or projective with respect to Mod-A, and every module is partially flat and projective with respect to the zero subcategory.
The aim of this paper is to prove that AN (respt. MA) is partially flat (resp. projective) with respect to the subcategory χ(A) of Mod-A. (In brief, we write these terms as χ(A)-flat and χ(A)-projective). This is established in Theorem II. In Theorem I a cancellation law related to the objects of χ(A) is proved.
@article{urn:eudml:doc:39961,
title = {Partially flat and projective modules.},
journal = {Extracta Mathematicae},
volume = {7},
year = {1992},
pages = {38-41},
mrnumber = {MR1203439},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39961}
}
Nauman, Syed Khalid. Partially flat and projective modules.. Extracta Mathematicae, Tome 7 (1992) pp. 38-41. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39961/