摘要：
Suppose F is a field, and n,p are integers with 1≤ pn( F) be the multiplicative semigroup of all n× n matrices over F, and let Mnp( F) be its subsemigroup consisting of all matrices with rank p at most. Assume that F and R are subsemigroups of Mn( F)
such that F\supseteq Mnp( F). A map f:F \rightarrow R is called a homomorphism if f(AB)=f(A)f(B) for any A,B∈ F. In particular, f is called an endomorphism if F= R. The structure of all homomorphisms from F to R (respectively, all endomorphisms of Mn( F)) is described.
中图分类号:
张显; 曹重光. HOMOMORPHISMS BETWEEN MULTIPLICATIVE SEMIGROUPS OF MATRICES OVER FIELDS[J]. 数学物理学报(英文版), 2008, 28(2): 301-306.
Zhang Xian; Cao Chongguang. HOMOMORPHISMS BETWEEN MULTIPLICATIVE SEMIGROUPS OF MATRICES OVER FIELDS[J]. Acta mathematica scientia,Series B, 2008, 28(2): 301-306.