Images of formal matrices of elements of matrix groups over associative rings

Abstract

The paper substantiates the image by formal matrices of some elements of linear groups over associative rings by using the properties of redundant and fixed modules. The form of images of elements of linear groups with respect to their homomorphisms in the group of automorphisms of modules over associative rings of 1, in which there are reversible elements 2 or 3, is shown. Using this approach, the authors described homomorphisms with the condition (*) of matrix groups over associative rings with 1. In particular, the isomorphisms of matrix groups over associative rings are homomorphisms with condition (*).

Keywords

• нерухомi та лишковi модулi, розклад модулiв
• iдемпотенти
• формальнi матрицi
• трансвекцiї
• комутатори
• гомоморфiзми лiнiйних груп над кiльцями