On ternary semifields

Tapan K. Dutta; Sukhendu Kar

Discussiones Mathematicae - General Algebra and Applications (2004)

  • Volume: 24, Issue: 2, page 185-198
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Tapan K. Dutta, and Sukhendu Kar. "On ternary semifields." Discussiones Mathematicae - General Algebra and Applications 24.2 (2004): 185-198. <http://eudml.org/doc/287678>.

@article{TapanK2004,
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.},
author = {Tapan K. Dutta, Sukhendu Kar},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {ternary semiring; prime ideal; maximal ideal; ternary semi-integral domain; ternary division semiring; ternary semifield; ternary semi-integral domains; ternary semifields},
language = {eng},
number = {2},
pages = {185-198},
title = {On ternary semifields},
url = {http://eudml.org/doc/287678},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Tapan K. Dutta
AU - Sukhendu Kar
TI - On ternary semifields
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2004
VL - 24
IS - 2
SP - 185
EP - 198
AB - 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.
LA - eng
KW - ternary semiring; prime ideal; maximal ideal; ternary semi-integral domain; ternary division semiring; ternary semifield; ternary semi-integral domains; ternary semifields
UR - http://eudml.org/doc/287678
ER -

References

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  1. [1] T.K. Dutta and S. Kar, On regular ternary semirings, Advances in Algebras, World Scientific Publ., Singapore 2003, 343-355. Zbl1041.16040
  2. [2] T.K. Dutta and S. Kar, On the Jacobson radical of a ternary semiring, Southeast Asian Bull. Math. 28 (2004), 1-13. Zbl1070.16048
  3. [3] T.K. Dutta and S. Kar, On prime ideals and prime radical of ternary semirings, Bull. Calcutta Math. Soc. 97 (2005), to appear. Zbl1098.16019
  4. [4] T.K. Dutta and S. Kar, On semiprime ideals and irreducible ideals of ternary semirings, (in preparation). Zbl1095.16021
  5. [5] J.S. Golan, Semirings and their Applications, Kluwer Academic Publishers, Dordrecht 1999. Zbl0947.16034
  6. [6] U. Hebisch and H.J. Weinert, Semirings - Algebraic Theory and Applications in Computer Science, World Scientific Publ. Co. Inc., River Edge, NJ, 1998. Zbl0934.16046
  7. [7] D.H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math. 59 (1932), 329-338. Zbl0004.19703
  8. [8] W.G. Lister, Ternary rings, Trans. Amer. J. Math. Soc. 154 (1971), 37-55. Zbl0216.06901
  9. [9] J. Łoś, On the extending of models I, Fund. Math. 42 (1955), 38-54. Zbl0065.00401
  10. [10] M.L. Santiago, Some contributions to the study of ternary semigroups and semiheaps, Ph.D. Thesis, University of Madras 1983. 
  11. [11] M.K. Sen and M.R. Adhikari, On maximal k-ideals of semirings, Proc. Amer. Math. Soc. 118 (1993), 699-703. Zbl0793.16040

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