Graph homomorphisms on rectangular matrices over division rings II. Issue 2 (1st February 2020)

• Record Type: Journal Article
• Authors: Huang, Li-Ping; Zhao, Kang
• Is Part Of: Linear & multilinear algebra. Volume 68:Issue 2(2020)
• Page Start: 391
• Page End: 409
• Publication Date: 2020-02-01
• Subjects: Graph homomorphism -- matrix -- division ring -- geometry of matrices; 15B33 -- 51A10 -- 51D20 -- 05C60; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1508403
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: Let D m × n be the set of m × n matrices over a division ring D . Two matrices A, B ∈ D m × n are adjacent if rank ( A − B ) = 1 . By the adjacency, D m × n is a connected graph. Suppose D, D ′ are division rings and m, n, m ′, n ′ ≥ 2 are integers. When | D | ≥ 4, we characterize the graph homomorphism ϕ : D n × n → D ′ m ′ × n ′ if ϕ ( 0 ) = 0 and there exists A 0 ∈ D n × n such that rank ( ϕ ( A 0 ) ) = n .