弱总体维数和模的自同态(英文)

Weak Global Dimension and Endomorphisms of Modules

英文关键词:weak global dimension, flat module, absolutely pure dimension, endomorphism.

中文摘要:

      本文用模的自同态，给出弱总体维数≤ｎ的环的特征，其中ｎ≥０．设Ｒ为环，部分地回答了下列问题：何时任意有限表现Ｒ－模Ｍ有无穷分解：０→Ｍ→Ｆ₀→Ｆ₁→…→Ｆ_n→…，其中每个Ｆ_i均是有限生成投射的，ｉ＝１，２，…？

英文摘要:

      Using endomorphisms of modules in this paper, we give the characterizations for rings of weak global dimension ≤n where n≥0. Let R be a ring, we partially answer the question: When has any finitely presented R-module M the nonfinitely resolution: 0→M→F₀→F₁→…→F_n→…, where each F_i is finitely generated projective, i=0,1,2,…?