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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

K. B. Prabhakara Rao
K. B. Prabhakara Rao
Affiliation:
Department of Mathematics Nagarjuna University A.C. College Campus Guntur, A.P. (India)
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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
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 2 , March 1978 , pp. 241 - 249
Copyright
Copyright © Australian Mathematical Society 1978

References

REFERENCES

Fuchs, L. (1963), Partially Ordered Algebraic Systems (Pergamon Press, Addison-Wesley).Google Scholar
Pilz, G. (1971), “Direct sums of ordered near-rings”, J. Algebra 18, 340–342.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