有限生成亚投射模范畴(英文)

The Category of Finitely Generated Meta-ProjectiveLeft R-Modules

英文关键词:meta-projective module  meta-Grothendieck group  category with factor-ization.

中文摘要:

      对一个QF环R,本文证明:其投射左R模范畴是因式分解范畴当且仅当gl.dim R≤1．进一步,若 P(_RR)＝P(R_R)＝0,则其通过左模而得到的亚 Crothendieck群与其通过右模而得到的亚Grothendieck群在同构意义下是一样的．还证明了有限生成亚投射左R－模范畴不仅是一个因式分解范畴而且是一个带积的具有小的骨架子范畴的范畴．

英文摘要:

      In this paper, it is shown that for a QF ring R, the category of projectiveleft R-modules is a category with factorization if and only if gl.dim R ≤1, moreover, if P(_RR) = P(R_R) = O,then the meta-Grothendieck groups obtained by left modules orby right modules are the same, up to isomorphism. It is also shown that the category of f.g. meta-pojective left R-modules is not only a category with factorization but also acategory with product such that it has a small skeletal subcategory.