HOMOMORPHISMS BETWEEN MULTIPLICATIVE SEMIGROUPS OF MATRICES OVER FIELDS  

作　　者：张显 曹重光 

机构地区：[1]School of Mathematical Science Heilongjiang University

出　　处：《Acta Mathematica Scientia》2008年第2期301-306,共6页数学物理学报（B辑英文版）

基　　金：the Chinese NSF under Grant No.10271021;the Younth Fund of Heilongjiang Province;the Fund of Heilongjiang Education Committee for Oversea Scholars under Grant No.1054HQ004

摘　　要：Suppose F is a field, and n, p are integers with 1 ≤ p 〈 n. Let Mn（F） be the multiplicative semigroup of all n × n matrices over F, and let M^Pn（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 M^Pn（F）. A map f ： F→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.Suppose F is a field, and n, p are integers with 1 ≤ p 〈 n. Let Mn（F） be the multiplicative semigroup of all n × n matrices over F, and let M^Pn（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 M^Pn（F）. A map f ： F→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.

关 键 词：HOMOMORPHISM ENDOMORPHISM multiplicative semigroup of matrices 

分 类 号：O152.7[理学—数学]