平面上保等价关系变换半群的格林关系

The Green's relation of transformation semigroup that preserves an equivalence on plane

设α=（mn），β=（st）∈R^2×1 .α～β→←m＋n=s＋t，则“～”是平面上向量间的一个等价关系。令：S={A∈R^2×2 V↓α，β∈R^2×1，α～β→←Aα-Aβ}。显然在矩阵乘法运算下S构成一个半群，讨论了S的格林关系。

Let α=（mn）,β=（st）∈R^2×1 denote α～β→←m＋n=s＋t,obviously the - is an equiva-lence between vectors on plane.Let S={A∈R^2×2 V↓α,β∈R^2×1,α～β→←Aα-Aβ}clearly S is a semigroup under matrix operation. The author studies the Green＇ s relation of S.