DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

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

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).
[5] J.S. Golan, Semirings and their Applications, Kluwer Academic Publishers, Dordrecht 1999.
[6] U. Hebisch and H.J. Weinert, Semirings - Algebraic Theory and Applications in Computer Science, World Scientific Publ. Co. Inc., River Edge, NJ, 1998.
[7] D.H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math. 59 (1932), 329-338.
[8] W.G. Lister, Ternary rings, Trans. Amer. J. Math. Soc. 154 (1971), 37-55.
[9] J. o\'s, On the extending of models I, Fund. Math. 42 (1955), 38-54.
[10] M.L. Santiago, Some contributions to the study of ternary semigroups and semiheaps, Ph.D. Thesis, University of Madras 1983.
[11] M.K. Sen and M.R. Adhikari, On maximal k-ideals of semirings, Proc. Amer. Math. Soc. 118 (1993), 699-703.

Received 13 January 2004
Revised 19 July 2004
Revised 29 November 2004

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