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ArticleOriginal scientific text

Title

Orderings and preorderings in rings with involution

Authors 1

Affiliations

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

Abstract

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.

Bibliography

  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.
Colloquium Mathematicum
2000/83/1
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Pages:
15-20
Main language of publication
English
Received
1999-03-23
Accepted
1999-07-28
Published
2000
Exact and natural sciences