This paper is a study on the invertibility of the commutator of scalar-idempotent elements and scalar-involutory elements of a unitary ring.

本文一个有单位元的环中两个倍幂元的换位子与两个倍对元的换位子的可逆性问题。

The necessary and sufficient conditions of similarity of two idempotent matrices are proved, the idempotency of linear combinations of two idempotent matrices is discussed.

摘要证明了数域上两个同阶幂似的充要条件是它们有同的秩；给出了幂的似标准型；讨论了两个幂的线性组仍是幂的充要条件。