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.
@article{bwmeta1.element.bwnjournal-article-cmv83i1p15bwm,
author = {Ismail Idris},
title = {Orderings and preorderings in rings with involution},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {15-20},
zbl = {0961.16020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv83i1p15bwm}
}
Idris, Ismail. Orderings and preorderings in rings with involution. Colloquium Mathematicae, Tome 84/85 (2000) pp. 15-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv83i1p15bwm/
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