Formal matrix rings: Automorphisms-Reference-Cited by-同舟云学术

Formal matrix rings: Automorphisms

Published:2023-06 Issue:04 Volume:33 Page:687-698
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

Krylov Piotr¹,Tuganbaev Askar²³

Affiliation:

1. National Research Tomsk State University, Algebra Department, Tomsk, Russia

2. National Research University “MPEI”, Mathematics Department, Moscow, Russia

3. Lomonosov Moscow State University, Algebra Department, Moscow, Russia

Abstract

Automorphism groups of formal matrix algebras with zero trace ideals are studied. Such an algebra is represented as a splitting extension of some ring by some nilpotent ideal. Using this extension, the study of the structure of the automorphism group of an algebra in a certain sense is reduced to the study of the structure of some its subgroups and quotient groups. Then the structure of these subgroups and factor groups is found. The case of formal triangular matrix rings is specially considered. At the end of the paper we study automorphisms of ordinary matrix rings. In this case, a well-known homomorphism from the group of outer automorphisms to the Picard group of a certain ring is used.

Funder

Russian Science Foundation

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196723500303

Reference32 articles.

1. Formal matrix rings and their isomorphisms

2. On certain classes of rings of formal matrices

3. Automorphism groups of generalized triangular matrix rings

4. Isomorphisms between strongly triangular matrix rings

5. Automorphism groups of algebras of triangular matrices