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 一类线性变换半群的格林关系 引用本文： 裴惠生,卢凤梅.一类线性变换半群的格林关系[J].数学研究及应用,2009,29(5):931-944. 作者姓名： 裴惠生  卢凤梅 作者单位： 信阳师范学院数学系, 河南 信阳 464000;安阳工业学院理学部, 河南 安阳 454900 摘    要： Let V be a linear space over a field F with finite dimension, L（V） the semigroup, under composition, of all linear transformations from V into itself. Suppose that V = V1 V2 ... Vm is a direct sum decomposition of V, where V1,V2,..., Vm are subspaces of V with the same dimension. A linear transformation f ∈ L（V） is said to be sum-preserving, if for each i （1 ≤ i ≤ m）, there exists some j （1 ≤ j ≤ m） such that f（Vi） Vj. It is easy to verify that all sum-preserving linear transformations form a subsemigroup of L（V） which is denoted by L （V）. In this paper, we first describe Green＇s relations on the semigroup L （V）. Then we consider the regularity of elements and give a condition for an element in L （V） to be regular. Finally, Green＇s equivalences for regular elements are also characterized. 关 键 词： 线性变换  变换半群  格林关系  直和分解  格林等价  空间域  有限维  虚拟机 收稿时间： 2007/5/18 0:00:00 修稿时间： 2007/11/22 0:00:00 Green's Relations on a Kind of Semigroups of Linear Transformations PEI Hui Sheng and LU Feng Mei.Green''s Relations on a Kind of Semigroups of Linear Transformations[J].Journal of Mathematical Research with Applications,2009,29(5):931-944. Authors: PEI Hui Sheng and LU Feng Mei Institution: Department of Mathematics, Xinyang Normal University, Henan 464000, China;Department of Science, Anyang Polytechnic College, Henan 454900, China Abstract: Let $V$ be a linear space over a field $F$ with finite dimension, $L(V)$ the semigroup, under composition, of all linear transformations from $V$ into itself. Suppose that $V=V_1 \oplus V_2 \oplus\cdots\oplus V_m$ is a direct sum decomposition of $V$, where $V_1,V_2,\ldots,V_m$ are subspaces of $V$ with the same dimension. A linear transformation $f\in L(V)$ is said to be sum-preserving, if for each $i\ (1\leq i\leq m)$, there exists some $j\ (1\leq j\leq m)$ such that $f(V_i)\subseteq V_j$. It is easy to verify that all sum-preserving linear transformations form a subsemigroup of $L(V)$ which is denoted by $L^{\oplus}(V)$. In this paper, we first describe Green's relations on the semigroup $L^{\oplus}(V)$. Then we consider the regularity of elements and give a condition for an element in $L^{\oplus}(V)$ to be regular. Finally, Green's equivalences for regular elements are also characterized. Keywords: linear spaces  linear transformations  semigroups  Green's equivalence  regular semigroups 本文献已被 维普 万方数据 等数据库收录！ 点击此处可从《数学研究及应用》浏览原始摘要信息 点击此处可从《数学研究及应用》下载免费的PDF全文