A note on relative flatness and coherence

作者：Zhang Xiaoxiang; Chen Jianlong

来源：Communications in Algebra, 2007, 35(11): 3321-3330.

DOI：10.1080/00927870701410645

• matrix subgroup
• M-coherent ring
• M-flat module

Let R be a ring and M a fixed right R-module. A new characterization of M-flatness is given by certain linear equations. For a left R-module F such that the canonical map M circle times(R) F -> Hom(R) (M*, F) is injective, where M* = Hom(R) (M, R), the M-flatness of F is characterized via certain matrix subgroups. An example is given to show that R need not be M-coherent even if every left R-module is M-flat. Moreover, some properties of M-coherent rings are discussed.

• 出版日期2007
• 单位东南大学