Natural partial order and finiteness conditions on semigroups of linear transformations with invariant subspaces

被引：9
|
作者：
Chaiya, Yanisa [1 ]
机构：
[1] Thammasat Univ Rangsit Campus, Fac Sci & Technol, Dept Math & Stat, Pathum Thani 12121, Thailand
来源：
SEMIGROUP FORUM | 2019年 / 99卷 / 03期
关键词：
Linear transformation semigroup; Invariant subspace; Natural partial order; Finiteness condition;
D O I：
10.1007/s00233-019-10012-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a vector space V and a subspace W of V, we consider the semigroup (under composition) S(V, W), consisting of all linear transformations on V which leave the subspace W invariant. In this paper, we characterize the natural partial order on S(V, W). In the partially ordered set, we determine the compatibility of their elements, and find all maximal and minimal elements. Also, we give necessary and sufficient conditions for S(V, W) to be factorizable, unit-regular and directly finite.
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页码：579 / 590
页数：12
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