欧氏空间中升序变换半群的格林关系和正则元

Green's Relations and Regularity for Semigroups of Order-Increasing Transformations on Euclidean Space

设L(R^n)表示n维欧氏空间R^n的所有线性变换构成的集合,||α||表示向量α的欧氏长度,由欧氏长度建立起向量间的序关系.令:O+(R^n)={f∈L(R^n)|(?)α∈R^n,||f(α)||≥||α||},则O+(R^n)是欧氏空间R^n的所有升序变换构成的集合,其在交换的合成运算下构成一个半群,讨论了O+(R^n)的格林关系和正则元.

Let L（R^n） be the set consisting of all linear transformations on n-dimensional Euclidean space R^n. Let ｜｜α｜｜ be the Euclidean length of vector α.According to the Euclid length of the vector, set up the order relation about the vector. Let O＋（R^n）={f∈L（R^n）}Vα∈R^n,｜｜f（a）｜｜≥｜｜α｜｜） be the set consisting of order-increasing transformation on Euclidean space Rn. Then O＋（Rn） is a semigroup under matrix operation. In this paper, we discuss Green＇s relations and regularity of elements for O＋（Rn）.