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HOMOMORPHISMS BETWEEN MULTIPLICATIVE SEMIGROUPS OF MATRICES OVER FIELDS

HOMOMORPHISMS BETWEEN MULTIPLICATIVE SEMIGROUPS OF MATRICES OVER FIELDS
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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.
作者 张显 曹重光
出处 《Acta Mathematica Scientia》 SCIE CSCD 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
关键词 HOMOMORPHISM ENDOMORPHISM multiplicative semigroup of matrices Homomorphism, endomorphism, multiplicative semigroup of matrices
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  • 1张显.交换整环上的上三角矩阵的保幂等的线性算子[J].新疆大学学报(自然科学版),1993,10(2):25-27. 被引量:9
  • 2S?nia P. Coelho.Automorphism groups of certain algebras of triangular matrices[J]. Archiv der Mathematik . 1993 (2)
  • 3Cao.Chongguang, Zhang Xian.Multiplicative semigroup automorphisms of upper triangular matrices overrings. Linear Algebra and Its Applications . 1998
  • 4Coelho S P.Automorphism groups of certain algebras of triangular matrices. Archiv der Mathematik . 1993
  • 5Jondrup S.Automorphisms and derivations of upper triangular matrix rings. Linear Algebra and Its Applications . 1995
  • 6Jondrup S.The Group of Automorphisms of Certain Subalgebras of Matrix Algebras. Journal of Algebra . 1991
  • 7Kezlan T P.A note on Algebra automorphisms of triangular matrices over commutative rings. Linear Algebra and Its Applications . 1990

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