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Extensions of strict partial orders in N-Groups
Part of:
Ordered sets
Published online by Cambridge University Press: 09 April 2009
Abstract
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An attempt is made to extend the theory of extensions of partial orders in groups to strict partially ordered N-groups. Necessary and sufficient conditions, for a strict partial order of an N-group to have a strict full extension, and for a strict partial order of an N-group to be an intersection of strict full orders, are obtained when the partially ordered near-ring N and the N-group G satisfy the condition (− x) n = − xn for all elements x in G and positive elements n in N.
MSC classification
Secondary:
06A75: Generalizations of ordered sets
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- Research Article
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- Copyright
- Copyright © Australian Mathematical Society 1978
References
REFERENCES
Fuchs, L. (1963), Partially Ordered Algebraic Systems (Pergamon Press, Addison-Wesley).Google Scholar
Radhakrishna, A. (1975), “On lattice ordered near-ring and nonassociative rings” (thesis submitted to the Department of Mathematics, Indian Institute of Technology, Kanpur, India).Google Scholar
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