Let M be a right R-module and N an infinite cardinal number. A right R-module N is called N-M-coherent if for any 0 ≤ A < B ≤ N, such that B/A → mR for some m ∈ M, if B/A is finitely generated, then B/A is N-fp...Let M be a right R-module and N an infinite cardinal number. A right R-module N is called N-M-coherent if for any 0 ≤ A < B ≤ N, such that B/A → mR for some m ∈ M, if B/A is finitely generated, then B/A is N-fp. A ring R is called N-M-coherent if RR is N-M-coherent. It is proved under some additional conditions that the N-product of any family of M-flat left R-modules is M-flat if and only if R is N-M-coherent. We also give some characterizations of N-M-coherent modules and rings.展开更多
基金the National Natural Science Foundation of China (No.10171082)
文摘Let M be a right R-module and N an infinite cardinal number. A right R-module N is called N-M-coherent if for any 0 ≤ A < B ≤ N, such that B/A → mR for some m ∈ M, if B/A is finitely generated, then B/A is N-fp. A ring R is called N-M-coherent if RR is N-M-coherent. It is proved under some additional conditions that the N-product of any family of M-flat left R-modules is M-flat if and only if R is N-M-coherent. We also give some characterizations of N-M-coherent modules and rings.
