Endomorphisms of matrix semigroups over division rings

被引：0

作者：

Peter Šemrl

机构：

[1] University of Ljubljana,Department of Mathematics

来源：

Israel Journal of Mathematics | 2008年 / 163卷

关键词：

Division Ring; Commutator Subgroup; Invertible Matrix; Principal Ideal Domain; Multiplicative Semigroup;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{D}$$ \end{document} be an arbitrary division ring and Mn(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{D}$$ \end{document}) the multiplicative semigroup of all n × n matrices over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{D}$$ \end{document}. We describe the general form of endomorphisms of Mn(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{D}$$ \end{document}).

引用

页码：125 / 138

页数：13

共 11 条

[1]

Dieudonné J.(1943)Les déterminants sur un corps non-commutatif Bulletin de la Société Mathématiqe de France 71 27-45

[2]

Djoković D. Ž.(1970)On homomorphisms of the general linear group Aequationes Math 4 99-102

[3]

Gluskin L. M.(1956)utomorphisms of multiplicative semigroups of matrix algebras Uspekhi Matematicheskikh Nauk 11 199-206

[4]

Halezov E. A.(1954)Automorphisms of matrix subgroups Doklady Akademii Nuauk SSSR 96 245-248

[5]

Halezov E. A.(1954)Isomorphisms of matrix semigroups Ivanov. Gos. Ped. Inst. Ucen. Zap. Fiz.-Mat. Nauk. 5 42-56

[6]

Jodeit M.(1969)Multiplicative maps of matrix semi-groups Archiv der Mathematik 20 10-16

[7]

Lam T. Y.(1993)Automorphisms of the poset of skew projections Journal of Functional Analysis 115 184-189

[8]

Ovchinnikov P. G.(1973)Multiplicative maps of matrix semigroups over Dedekind rings Archiv der Mathematik 24 25-29

[9]

Pierce S.(2004)Hua’s fundamental theorem of the geometry of matrices Journal of Algebra 272 801-837

[10]

Šemrl P.(2006)Maps on idempotent matrices over division rings Journal of Algebra 298 142-187

← 1 2 →