Cohen's Theorem for a Class of Semirings

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Authors

  • M. R. Adhikari
     Department of Mathematics, University of Burdwan, Burdwan ,IN
  • M. K. Sen
     Department of Pure Mathematics, Calcutta University, Calcutta ,IN

Keywords:

Semiring, Noetherian semiring, Cohen's Theorem, Congruence

Abstract

The main aim of this paper is to show that Cohen's Theorem is valid for AC-Noetherian semirings.

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Published

1995-01-01

How to Cite

Adhikari, M. R., & Sen, M. K. (1995). Cohen’s Theorem for a Class of Semirings. Indian Science Cruiser, 9(1), 28–33. Retrieved from https://informaticsjournals.co.in/index.php/ISC/article/view/42802

Issue

Volume 9, Issue 1, 1995

Section

Research Report

 

References

IS Cohen, Commutative nngs with restricted minimum condition, Duke Math J, 27-42, 1950

P J Allen, Cohen's theorem for a class of Noetherian semirings, Puhl Math Debrecen, 17, 169-171, 1970

M K Sen and M R Adhikari, A generalization of Cohen's theorem in additive inverse semirings, Internatwnl J of Math and Math Sc, USA (to appear)

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

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

MR Adhikari, Groups, nngs and semirings with applications, Orient Longman (to appear)

H S Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold. Bull Amer Math Soc 40, 914-920, 1934