中国科学A辑(英文版)
中國科學A輯(英文版)
중국과학A집(영문판)
SCIENCE IN CHINA
2002年
8期
1025-1037
,共13页
division ring%involution%generalized quaternion%hermitian matrix%adjacency
Let D be a division ring which possesses an involution a→ā. Assume that F = {a∈D|a=ā} is a proper subfield of D and is contained in the center of D. It is pointed out that if D is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two, D is a separable quadratic extension of F. Thus the trace map Tr: D→F,hermitian matrices over D when n≥3 and now can be deleted. When D is a field, the fundamental theorem of 2×2 hermitian matrices over D has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two.
