Discussiones Mathematicae General Algebra and Applications 24(2) (2004) 185-198
doi: 10.7151/dmgaa.1084

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ON TERNARY SEMIFIELDS

Tapan K. Dutta and Sukhendu Kar

Department of Pure Mathematics
University of Calcutta
35, Ballygunge Circular Road, Kolkata-700019, India

e-mail: duttatapankumar@yahoo.co.in
e-mail: karsukhendu@yahoo.co.in

Abstract

In this paper, we introduce the notion of ternary semi-integral domain and ternary semifield and study some of their properties.In particular we also investigate the maximal ideals of the ternary semiring Z-0.

Keywords: ternary semiring, prime ideal, maximal ideal, ternary semi-integral domain, ternary division semiring, ternary semifield.

2000 Mathematics Subject Classification: 16Y30, 16Y60, 20N10.

References

[1] T.K. Dutta and S. Kar, On regular ternary semirings, p. 343-355 in: Advances in Algebras, World Scientific Publ., Singapore 2003.
[2] T.K. Dutta and S. Kar, On the Jacobson radical of a ternary semiring, Southeast Asian Bull. Math. 28 (2004), 1-13.
[3]T.K. Dutta and S. Kar, On prime ideals and prime radical of ternary semirings, Bull. Calcutta Math. Soc. 97 (2005), to appear.
[4] T.K. Dutta and S. Kar, On semiprime ideals and irreducible ideals of ternary semirings, (in preparation).
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Received 13 January 2004
Revised 19 July 2004
Revised 29 November 2004