分次非奇异三角矩阵环

设Ω是一个适合左（右）消去律的Monoid, S=_x∈ΩS_x和T =_x∈ΩT_x是两个有1的Ω分次环， B=_SB_T=_x∈ΩB_x是一个Ω分次（S，T）双模， R是由它们确定的Ω分 次三角矩阵环. 证明了当_SB是分次忠实模时, R是分次非奇异环当且仅当T是分 次非奇异环, B_T是分次非奇异模.

Graded nonsingular triangular matrix rings

Let Ω be a multiplicative left(right) cancellative monoid, S=_x∈ΩS_x and T=_x∈ΩT_x be two Ω-graded rings with 1, and B=_SB_T=_{x∈ΩBx be a Ω-graded (S,T)-bimodule, R is the graded triangular matrix ring determined by S,T and SBT. It is shown that if SB is graded faithful then R is a graded nonsingular ring if and only if T is a graded nonsingular ring and BT is a graded nonsin gular module.}