关于除环的伪理想

M.K.Sen于1976年推广环的理想概念,定义了伪理想,并用依理想来研究除环、域和正则环。侯国荣1983年又推广伪理想,建立n—伪理想,得到了更好的结果。本文则证明了:非交换除环和有限域无真伪理想,因而文关于除环的几乎全部结果都是平凡的。我们还证明了非交换除环无真n—伪理想,给出了有限域无真n—伪理想的充分必要条件。文中讨论了无限域的伪理想,得到了关于除环结构的几个有用结果。

On pseudo ideals of division rings

M. K- Sen defined a concept pseudo ideal of a riog in 1976, and use it to study division rings, fields and reqular rings. In this paper we have proved that does not exist any proper pseudo ideal in a non-Commutative division r ring and a finite field. Hence it is trivial that M- K- Sen's results on pseudo ideals of division rings, we have studed pseudo ideals of infinite fields, obt obtained some useful results on stucture of division rings .