the National Natural Science Foundation of China (No.10171082);TRAPOYT (No.200280);Yong Teachers Research Foundation of NWNU (No.NWNU-QN-07-36)
Let R be a ring. Recall that a right R-module M (RR, resp.) is said to be a PS-module (PS-ring, resp.) if it has projective socle. M is called a CESS-module if every complement summand in M with essential socle is a d...
the National Natural Science Foundation of China (No.10171082)
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...
the National Natural Science Foundation of China (No. 10171082); the Natural Science Foundation of Gansu Province (No. 3ZSA061-A25-015) and the Scientific Research Fund of Gansu Provincial Education Department (Nos. 06021-21; 0410B-09).
For a monoid M, we introduce M-McCoy rings, which are generalization of McCoy rings, and we investigate their properties. Every M-Armendariz ring is M-McCoy for any monoid M. We show that R is an M-McCoy ring if and o...
the National Natural Science Foundation of China(10171082)
It is well-known that a ring R is right Noetherian if and only if every direct sum of injective right R-modules is injective. In this paper, we will characterize Ne-Noetherian rings and U-Noetherian rings by Ne-inject...
the National Natural Science Foundation of China(10171082)and by NWNU-KJCXGC212
This paper investigates the characterizations of monoids over which all strongly flat right S-acts are regular. It is shown that all strongly flat right S-acts are regular if and only if S is a right PSF monoid and ev...