Fuzzy Maximal Ideals of ADL's


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Authors

  • Ch. Santhi Sundar Raj Department of Engineering Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India
  • A. Natnael Teshale Department of Mathematics, University of Gondar, Gondar, Ethiopia
  • U. M. Swamy Department of Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India

Keywords:

Almost Distributive Lattice (ADL), Maximal L-fuzzy ideal, L-fuzzy Maximal ideal, Complete Lattice

Abstract

In this paper, we determine all maximal $L$-fuzzy ideals of a given ADL $A$ with a maximal element by establishing a one-to-one correspondence between maximal $L$-fuzzy ideals of $A$ and the pairs $(M,\alpha)$, where $M$ is a maximal ideal of $A$ and $\alpha$ is a dual atom in a complete lattice $L$ satisfying the infinite meet distributive law. Also, the notion of an $L$-fuzzy maximal ideal of $A$ is introduced and characterized.

 

 

Author Biographies

Ch. Santhi Sundar Raj, Department of Engineering Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India

 

 

A. Natnael Teshale, Department of Mathematics, University of Gondar, Gondar, Ethiopia

 

 

U. M. Swamy, Department of Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India

 

 

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Published

01-03-2018

How to Cite

Ch. Santhi Sundar Raj, A. Natnael Teshale, & U. M. Swamy. (2018). Fuzzy Maximal Ideals of ADL’s. International Journal of Mathematics And Its Applications, 6(1 - D), 819–824. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/1145

Issue

Vol. 6 No. 1 - D (2018)

Section

Research Article

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