Multiplicative Derivations on Rank-s Matrices for Relatively Small s

作者：Xu, Xiaowei^*; Xie, Baochuan; Wang, Yanhua; Zhao, Zhibing

来源：ALGEBRA COLLOQUIUM, 2023, 30(02): 281-292.

DOI：10.1142/S1005386723000226

• multiplicative derivations
• rank-s matrices
• singular matrices

In this paper, we describe multiplicative derivations on the set of all rank-s matrices of M-n(K) over a field K with a relatively small integer s. Concretely, for fixed integers n; s satisfying 1 <= s <= n/2 and n >= 2, we prove that if a map delta : M-n(K) -> M-n(K) satisfies delta(xy) = delta(x)y + x delta(y) for any two rank-s matrices x, y is an element of M-n(K), then there exists a derivation D of M-n(K) such that delta(x) = D(x) for each rank-k matrix x is an element of M-n(K) with 0 <= k <= s. As an application, we prove that a multiplicative derivation on a special subset of M-n(K) must be a derivation.

• 单位
  吉林大学