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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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Certain ordered algebraic structures
by
J. Hanumanthachari
Dept. of Mathematics, S.V.University, Tirupati - 517 502 , (A.P) ,INDIA

Totally ordered semirings whose multiplicative structures are r.n.t.o and satisfy max-R or min-R are considered. Also totally ordered semirings whose additive structures are r.n.t.o. and satisfy max-R or min-R condition are discussed. Totally ordered rings satisfying an analogous property of the usual integers are considered. The Author of this talk calls this property as "Integral Multiple Property(IMP)". In fact O-Archimedean property under addition and non negetively ordered property under multiplication are equivalent to IMP. If the multiplicative sturcture of a totally ordered ring is nonnegetively ordered then the ring is imbeddable in an ordered field. Some of the fundamental properties related to the well-ordered principles are also discussed.

Date received: February 10, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadx-24.