The main results of this paper are following theorems: (1)A left A-injective ring satisfying the ascending chain condition on right annihilator is QF ring. (2)A left A-injective ring satisfying the ascending hain cond...The main results of this paper are following theorems: (1)A left A-injective ring satisfying the ascending chain condition on right annihilator is QF ring. (2)A left A-injective ring satisfying the ascending hain condition on left annihilator is QF ring. (3)If R satisfies the following conditions: (ⅰ) r(A∩B)=r(A)+r(B), for each pair of left ils A,B;(ⅱ) rl(I)=I, for every right ideal I. Then R is semiperfect ring and has essential left s. In particular, any right CF left A-injective (or E(_RR) is projective left R-module) is QF ring展开更多
We give a necessary and sufficient condition for the fundamental group homomorphism of a map between CW-complexes(manifolds) to induce partial homology equivalences. As applications, we obtain characterizations of fun...We give a necessary and sufficient condition for the fundamental group homomorphism of a map between CW-complexes(manifolds) to induce partial homology equivalences. As applications, we obtain characterizations of fundamental groups of homology spheres and Moore manifolds. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.展开更多
文摘The main results of this paper are following theorems: (1)A left A-injective ring satisfying the ascending chain condition on right annihilator is QF ring. (2)A left A-injective ring satisfying the ascending hain condition on left annihilator is QF ring. (3)If R satisfies the following conditions: (ⅰ) r(A∩B)=r(A)+r(B), for each pair of left ils A,B;(ⅱ) rl(I)=I, for every right ideal I. Then R is semiperfect ring and has essential left s. In particular, any right CF left A-injective (or E(_RR) is projective left R-module) is QF ring
基金supported by National Natural Science Foundation of China(Grand No.10901151)RDF-13-02-08 of Xi’an Jiaotong-Liverpool University
文摘We give a necessary and sufficient condition for the fundamental group homomorphism of a map between CW-complexes(manifolds) to induce partial homology equivalences. As applications, we obtain characterizations of fundamental groups of homology spheres and Moore manifolds. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.
