In this paper, the induced group homomorphism was studied. It is proved that for any ideal I of a ring R contained in J(R), K 0(π):K 0(R)→K 0(R/I) is isomorphic if and only if K 0(π) + is a sem...In this paper, the induced group homomorphism was studied. It is proved that for any ideal I of a ring R contained in J(R), K 0(π):K 0(R)→K 0(R/I) is isomorphic if and only if K 0(π) + is a semigroup isomorphism; characterizations are given for the semilocal rings being semiperfect.展开更多
In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and Kp algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of Kp algebras admit...In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and Kp algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of Kp algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul algebra or to be a quasi-Kp algebra.展开更多
设R是环,证明了:1)R是右Noether,右单J-内射环,且Sr≤eRR或R是右Goldie,右单J-内射环,且Sr≤eRR,则R是右QF环;2)如果R是左完全环且当Rk或kR是单左或右理想时,r(k)是有限生成的,则R是右QF环.推广了文献[2]中Nicholson W K,Park J K,Yousi...设R是环,证明了:1)R是右Noether,右单J-内射环,且Sr≤eRR或R是右Goldie,右单J-内射环,且Sr≤eRR,则R是右QF环;2)如果R是左完全环且当Rk或kR是单左或右理想时,r(k)是有限生成的,则R是右QF环.推广了文献[2]中Nicholson W K,Park J K,Yousif M F的相关结论并使著名的Faith猜想有了新的进展.展开更多
文摘In this paper, the induced group homomorphism was studied. It is proved that for any ideal I of a ring R contained in J(R), K 0(π):K 0(R)→K 0(R/I) is isomorphic if and only if K 0(π) + is a semigroup isomorphism; characterizations are given for the semilocal rings being semiperfect.
基金Supported by the National Natural Science Foundation of China(10971188)the Zhejiang ProvincialNatural Science Foundation of China(J20080154)
文摘In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and Kp algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of Kp algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul algebra or to be a quasi-Kp algebra.
文摘设R是环,证明了:1)R是右Noether,右单J-内射环,且Sr≤eRR或R是右Goldie,右单J-内射环,且Sr≤eRR,则R是右QF环;2)如果R是左完全环且当Rk或kR是单左或右理想时,r(k)是有限生成的,则R是右QF环.推广了文献[2]中Nicholson W K,Park J K,Yousif M F的相关结论并使著名的Faith猜想有了新的进展.
