特征不为2的欧氏环上不同阶矩阵半群的同态

HOMOMORPHISMS OF MATRIX SEMIGROUPS OVER EUCLIDEAN DOMAINS WITHCHARACTERSTIC NOT 2

设 R、S都是特征不为 2的欧氏环 ,φ是矩阵半群 Mn( R)到 Mm( S)的同态 .本文在 n≥ 3,n>m的限制下 ,确定 φ的形式为 φ( X) =P( σdet X Om2 Im3 ) P- 1, X∈ Mn( R) ,其中 P∈ GLm( S) ,σ:R→ GLm1( S)∪ {Om1}是乘法半群同态 ,m=m1+ m2 + m3.

Let R and S all be Euclidean domains with characteristic not 2, φ a homomorphism from Matrix semigroup M n(R) to M m(S) with n≥3 and n>m, we obtain the form that φ(X)=P(σ(detX)O m 2 I m 3 )P -1 ,X∈M n(R), where P∈GL m(S), σ:R→GL m 1 (S)∪{O m 1 } is a homomorphism, m=m 1+m 2+m 3.