On Maximal K- Ideals of Semirings

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Authors

  • M R Adhikari
     Department of Mathematics University of Burdwan 713104. West Bengal ,IN
  • Sanjib Kumar Das
     Department of Mathematics, S S Mahavidyalaya, Ajodhya, Howrah ,IN

Keywords:

Semirings, k-ideal, h-ideal. Bourne Congruence and lizuka congruence

Abstract

The k- ideals of semirings were investigated by M K Sen and M R Adhikari' I In this paper, for a semiring S with commutative addition, conditions are considered such that S has non-trivial h-ideals or maximal h-ideals, among others by the help of lizuka Congruence class semiring S/A defined by an ideal A of S. Moreover, semirings with descending chain conditions are studied.

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Published

1995-03-13

How to Cite

Adhikari, M. R., & Das, S. K. (1995). On Maximal K- Ideals of Semirings. Indian Science Cruiser, 9(3), 23–30. Retrieved from https://informaticsjournals.com/index.php/ISC/article/view/42813

Issue

Vol 9, No 3 (1995)

Section

Research Report

 

References

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M K Sen and M R Adhikari, On maximal k-ideals of semirings, Proc Amer Math Soc. 118(3), 699-703, 1993.

H J Weinert, Uber Halbringe and Halbkorperl, ACTA Math Acad Sc Hunger, 13, 365-378, 1962.

M Henriksen, Ideals in semirings with commulative addition, Amer Math Soc Notices 5, 321, 1958.

K lizuka, On the Jacobson radical of a semiring, Tohoku Math J 11(2); 409-421, 1959.

S Bourne, The Jacobson radical of a semiring, Proc Nat Acad Sci (USA) 37, 169-170, 1951.

S Bourne and H Zassenhaus, On the radicals of a semiring, Proc Nat Acad Sci, 44, 907-914, 1958.

D R Latorre, On h-idea!s and k-ideals in hemirings. Pub Math Debrecen, 14, 9-13, 1967.

M R Adhikari and M K Sen, Cohen's Theorem for a class of semirings, Indian Sc Cr 9(1), 28-33, 1995.

M K Sen and M R Adhikari, On division hemirings. Bull Cal Math Soc, 83, 267-274, 1991.

M R Adhikari, Groups, rings and semirings with applications (In Press).

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