分次三角矩阵环的性质

Properties of Graded Triangular Matrix Rings

给定两个分次环 R = x∈ MRx,A = x∈ MAx和一个分次双模 V =RVA= x∈ MVx,可以得到一个分次三角矩阵环 T=R V0 A = x∈ MRx Vx0 Ax.对分次强π正则性、弱分次直有限性和与分次 J根密切相关的几个分次环性质 ,讨论了 T与 R,A之间的性质关系 .

Given two graded rings R=x∈MR_x, A=x∈MA_x and one graded bimodule V=_RV_A=x∈MV_x we can obtain a graded trigangular matrix ring T=RV0A=x∈MR_xV_x0A_x. In this paper are discussed the property relations among R,A and T for graded strongly π-regularity, weakly graded direct finiteness and some graded ring properties in close relationship with graded J-radical.