Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

On Maximal K- Ideals of Semirings


Affiliations
1 Department of Mathematics University of Burdwan 713104. West Bengal, India
2 Department of Mathematics, S S Mahavidyalaya, Ajodhya, Howrah, India
     

   Subscribe/Renew Journal


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.

Keywords

Semirings, k-ideal, h-ideal. Bourne Congruence and lizuka congruence
User
Subscription Login to verify subscription
Notifications
Font Size

  • M K Sen and M R Adhikari, On k-ideals of stmmngs, Jnternationat J of Math and Math Sciences (USA), 15 (2), 347-350, 1992.
  • 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).

Abstract Views: 174

PDF Views: 0




  • On Maximal K- Ideals of Semirings

Abstract Views: 174  |  PDF Views: 0

Authors

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

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.

Keywords


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

References