Multiplicative semigroup automorphisms of upper triangular matrices over rings Original Research Article

Suppose R is a ring with 1 and C a central subring of R. Let Tn(R) be the C-algebra of upper triangular n × n matrices over R. Recently several authors have shown that if R is sufficiently well behaved, then every C-automorphism of Tn(R) is the composites of an inner automorphism and an automorphism induced from a C-automorphism of R (see [1–5]). To generalize these results, in this paper we prove that if n greater-or-equal, slanted 2 and R is a semiprime ring or a ring in which all idempotents are central, then f : Tn(R) → Tn(R) (Tn(R) is only regarded as a multiplicative semigroup) is a multiplicative semigroup automorphism if and only if there exist a nonsingular matrix P in Tn(R) and a ring automorphism τ of R such that imagef(A) = P−1AτP for allA = (aij)n×n set membership, variant τn(R),