The lattice of L-ideals of a ring is modular

  • Authors:
  • Iffat Jahan

  • Affiliations:
  • Department of Mathematics, Ramjas College, University of Delhi, Delhi 110007, India

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2012

Quantified Score

Hi-index 0.20

Visualization

Abstract

In this paper, we extend the notion of a tip-extended pair of fuzzy subgroups to L-ideals of a ring. We prove that the sum of two tip-extended L-ideals of an arbitrary pair of L-ideals of a ring is the least L-ideal containing the union of the given L-ideals. Using this construction of join of L-ideals, we prove that the lattice of all L-ideals of a given ring is modular.