Let T=RM NS (θ,φ) and θ=0. We use a complete different technique to obtain the generalize results for K 0(T), i.e., K 0(T/I)K 0(R)K 0(S/NM) and K 0(T/J(T)) K 0(R/J(R))K(S/J(S)).
While the formulations of localization rank and stably free rank are given, the characterizations of elements are obtained for a class of VN regular ring. For a ring R, the characters of some properties of K0R are als...While the formulations of localization rank and stably free rank are given, the characterizations of elements are obtained for a class of VN regular ring. For a ring R, the characters of some properties of K0R are also given in terms of the state space of K0.展开更多
Sharpe once gave a beautiful 4-term decomposition LPLU for infinite Steinberg group; recently Li Fu-an has given a sufficient and necessary condition for 4-term decomposition LWLU of finite Steinberg group over commut...Sharpe once gave a beautiful 4-term decomposition LPLU for infinite Steinberg group; recently Li Fu-an has given a sufficient and necessary condition for 4-term decomposition LWLU of finite Steinberg group over commutative rings. The present note extends the result of [2] to non-commutative rings and studies the decomposition of a finite Steinberg group over local rings.展开更多
Suppose R be a commutative ring with an identity element 1. Tong Wenting hasstudied PF rings in ref.[1]. A ring R is called a PF ring if every finitely generatedprojective R-module is free. In this note, we construct ...Suppose R be a commutative ring with an identity element 1. Tong Wenting hasstudied PF rings in ref.[1]. A ring R is called a PF ring if every finitely generatedprojective R-module is free. In this note, we construct a new abelian group X(R). Asa ring, we will prove X(R) is a PF ring.展开更多
文摘Let T=RM NS (θ,φ) and θ=0. We use a complete different technique to obtain the generalize results for K 0(T), i.e., K 0(T/I)K 0(R)K 0(S/NM) and K 0(T/J(T)) K 0(R/J(R))K(S/J(S)).
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 19901009) NSF of Guangdong Province (Grant Nos. 970472, 000463).
文摘While the formulations of localization rank and stably free rank are given, the characterizations of elements are obtained for a class of VN regular ring. For a ring R, the characters of some properties of K0R are also given in terms of the state space of K0.
文摘Sharpe once gave a beautiful 4-term decomposition LPLU for infinite Steinberg group; recently Li Fu-an has given a sufficient and necessary condition for 4-term decomposition LWLU of finite Steinberg group over commutative rings. The present note extends the result of [2] to non-commutative rings and studies the decomposition of a finite Steinberg group over local rings.
文摘Suppose R be a commutative ring with an identity element 1. Tong Wenting hasstudied PF rings in ref.[1]. A ring R is called a PF ring if every finitely generatedprojective R-module is free. In this note, we construct a new abelian group X(R). Asa ring, we will prove X(R) is a PF ring.
