Dense Subsemigroups of Matrix Semigroups and Semigroups of Linear Transformations

• 来源期刊: 代数集刊（英文版）
• 关键词: matrix semigroups semigroups of linear transformations dense sub-semigroups
• 年，卷（期）: 2002,（3）
• 页码范围: 337-343
• 页数: 7页
• 语种: 英文

摘要

Let V be a vector space over a field F = (F, +, .), F* = F\{0}, LF(V)the semigroup of all linear transformations of V into itself under composition, and Mn(F) the multiplicative full n × n matrix semigroup over F. In this paper, it is proved that the semigroup Mn(F) has a proper dense subsemigroup if and only if(F*, .) has an element of infinite order. Also, the semigroup LF(V) has a proper dense subsemigroup if and only if dimF V = ∞ or (F*, .) has an element of infinite order.