Partially flat and projective modules.

Nauman, Syed Khalid. "Partially flat and projective modules.." Extracta Mathematicae 7.1 (1992): 38-41. <http://eudml.org/doc/39961>.

@article{Nauman1992,
abstract = {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.},
author = {Nauman, Syed Khalid},
journal = {Extracta Mathematicae},
keywords = {Anillos; Módulos; Categoría de módulos; Módulo estático},
language = {eng},
number = {1},
pages = {38-41},
title = {Partially flat and projective modules.},
url = {http://eudml.org/doc/39961},
volume = {7},
year = {1992},
}

TY - JOUR
AU - Nauman, Syed Khalid
TI - Partially flat and projective modules.
JO - Extracta Mathematicae
PY - 1992
VL - 7
IS - 1
SP - 38
EP - 41
AB - 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.
LA - eng
KW - Anillos; Módulos; Categoría de módulos; Módulo estático
UR - http://eudml.org/doc/39961
ER -