Orderings and preorderings in rings with involution

• Autorzy: Ismail M. Idris
• Języki publikacji: EN

Abstrakty

EN

The notions of a preordering and an ordering of a ring R with involution are investigated. An algebraic condition for the existence of an ordering of R is given. Also, a condition for enlarging an ordering of R to an overring is given. As for the case of a field, any preordering of R can be extended to some ordering. Finally, we investigate the class of archimedean ordered rings with involution.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 83
• Numer: 1
• Strony: 15-20

Daty

wydano

2000

otrzymano

1999-03-23

poprawiono

1999-07-28

Twórcy

autor

Ismail M. Idris

• Mathematics Department, Faculty of Science, Ain-Shams University, Cairo, Egypt

Bibliografia

• [1] M. Chacron, C-orderable division rings with involution, J. Algebra 75 (1982), 495-521.
• [2] S. S. Holland, Strong ordering of *-fields, J. Algebra 101 (1986), 16-46.
• [3] I. M. Idris, Jordan ordering of a division ring with involution, Arabian J. Sci. Engrg. 14 (1989), 527-535.