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

本文研究在一有的环中倍幂等的换子与倍对的换子的可逆性问题。

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

摘要证明了数域同阶幂等阵相似的充要条件是它们有相同的秩；给出了幂等阵的相似标准型；讨论了幂等阵的线性组仍是幂等阵的充要条件。