# Orderings and preorderings in rings with involution

Colloquium Mathematicae (2000)

- Volume: 83, Issue: 1, page 15-20
- ISSN: 0010-1354

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topIdris, Ismail. "Orderings and preorderings in rings with involution." Colloquium Mathematicae 83.1 (2000): 15-20. <http://eudml.org/doc/210769>.

@article{Idris2000,

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.},

author = {Idris, Ismail},

journal = {Colloquium Mathematicae},

keywords = {Archimedean rings; orderings; rings with involutions; extendibility; symmetric elements; commutative subrings},

language = {eng},

number = {1},

pages = {15-20},

title = {Orderings and preorderings in rings with involution},

url = {http://eudml.org/doc/210769},

volume = {83},

year = {2000},

}

TY - JOUR

AU - Idris, Ismail

TI - Orderings and preorderings in rings with involution

JO - Colloquium Mathematicae

PY - 2000

VL - 83

IS - 1

SP - 15

EP - 20

AB - 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.

LA - eng

KW - Archimedean rings; orderings; rings with involutions; extendibility; symmetric elements; commutative subrings

UR - http://eudml.org/doc/210769

ER -

## References

top- [1] M. Chacron, C-orderable division rings with involution, J. Algebra 75 (1982), 495-521. Zbl0482.16013
- [2] S. S. Holland, Strong ordering of *-fields, J. Algebra 101 (1986), 16-46. Zbl0624.06024
- [3] I. M. Idris, Jordan ordering of a division ring with involution, Arabian J. Sci. Engrg. 14 (1989), 527-535. Zbl0693.06016

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