A note on idempotence-preserving maps

作者：Tang Xiao Min^*; Xu Jin Li; Cao Chong Guang

来源：Linear and Multilinear Algebra, 2008, 56(4): 399-414.

DOI：10.1080/03081080701403840

• field
• characteristic
• idempotence
• preserving
• homogeneous

Let M-n(F) be the space of all n x n matrices over a field F of characteristic not 2, and let P-n(F) be the subset of M-n(F) consisting of all n x n idempotent matrices. We denote by phi(n)(F) the set of all maps from M-n(F) to itself satisfying A-lambda B is an element of P-n(F) implies empty set(A) -lambda empty set (B) is an element of P-n(F) for every A, B is an element of M-n(F) and lambda is an element of 2 F. In this note, we prove that empty set is an element of phi(n)(F) if and only if there exist delta is an element of {0, 1} and an invertible matrix P is an element of M-n(F) such that either empty set(A) = delta PAP(-1) for every A is an element of M-n(F), or empty set (A)=delta PA(T)P(-1) for every A is an element of M-n(F). This improves the result of some related references.

• 出版日期2008
• 单位黑龙江大学