• Bulletin of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.973-981
• /
• 2021

Let R be a commutative ring with identity 1, n ≥ 3, and let 𝒯_n(R) be the linear Lie algebra of all upper triangular n × n matrices over R. A linear map 𝜑 on 𝒯_n(R) is called to be strong commutativity preserving if [𝜑(x), 𝜑(y)] = [x, y] for any x, y ∈ 𝒯_n(R). We show that an invertible linear map 𝜑 preserves strong commutativity on 𝒯_n(R) if and only if it is a composition of an idempotent scalar multiplication, an extremal inner automorphism and a linear map induced by a linear function on 𝒯_n(R).

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.711-713
• /
• 2006

Let R be a semiprime ring and f be an endomorphism on R. If f is a strong commutativity preserving (simply, scp) map on a non-zero ideal U of R, then f is commuting on U.