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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.