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)).
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
The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-W...The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator Mb(z) is similar to n + 1 copies of the Bergman shift if and only if B(z) is an n + 1-Blaschke product. Prom the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K0-group term.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)).
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.
基金the National Natural Science Foundation of China (Grant No. 10571041)
文摘The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator Mb(z) is similar to n + 1 copies of the Bergman shift if and only if B(z) is an n + 1-Blaschke product. Prom the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K0-group term.
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.
