On ternary semifields

Tapan Dutta; Sukhendu Kar

ArticleOriginal scientific text

Title

On ternary semifields

Authors ¹, ¹

Affiliations

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

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

ENG

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

T.K. Dutta and S. Kar, On regular ternary semirings, Advances in Algebras, World Scientific Publ., Singapore 2003, 343-355.
T.K. Dutta and S. Kar, On the Jacobson radical of a ternary semiring, Southeast Asian Bull. Math. 28 (2004), 1-13.
T.K. Dutta and S. Kar, On prime ideals and prime radical of ternary semirings, Bull. Calcutta Math. Soc. 97 (2005), to appear.
T.K. Dutta and S. Kar, On semiprime ideals and irreducible ideals of ternary semirings, (in preparation).
J.S. Golan, Semirings and their Applications, Kluwer Academic Publishers, Dordrecht 1999.
U. Hebisch and H.J. Weinert, Semirings - Algebraic Theory and Applications in Computer Science, World Scientific Publ. Co. Inc., River Edge, NJ, 1998.
D.H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math. 59 (1932), 329-338.
W.G. Lister, Ternary rings, Trans. Amer. J. Math. Soc. 154 (1971), 37-55.
J. Łoś, On the extending of models I, Fund. Math. 42 (1955), 38-54.
M.L. Santiago, Some contributions to the study of ternary semigroups and semiheaps, Ph.D. Thesis, University of Madras 1983.
M.K. Sen and M.R. Adhikari, On maximal k-ideals of semirings, Proc. Amer. Math. Soc. 118 (1993), 699-703.

Title

On ternary semifields

Affiliations

Abstract

Keywords

Bibliography