分次遗传三角矩阵环

Graded Hereditary Triangular Matrix Rings

设Ω是一个具有左 (右 )消去律的Monoid .给定两个有 1的Ω 分次环A = x∈MAx 和B = x∈MBx 以及一个Ω 分次 (A ,B) 双模V =SVT = x∈MVx,由它们确定一个Ω 分次三角矩阵环T =AV0B = x∈MAx Vx0Bx.本文证明T是分次右遗传环当且仅当 (i) A和B都是分次右遗传环 ;(ii) AV是平坦模 ;(iii)对任何K ≤grAA,(V/KV) B 是投射模 .

Let Ω be a multiplicative left(right) cancellative Monoid.Given two Ω- graded rings with 1 , A=x∈MA_x and B=x∈MB_x ,and a Ω- graded (A,B) -bimodule V= _SV_T=x∈MV_x, they determind a graded triangular matrix ring T=AV 0B=x∈MA_xV_x 0B_x. In this paper,we show that T is graded right hereditary ring if and only if (i) A and B are both graded right hereditary;(ii) _AV is flat;(iii) (V/KV)_B is projective for all K≤grA_A.