IJPAM: Volume 89, No. 3 (2013)

ON T-FUZZY ESSENTIAL IDEALS OF RINGS

Ujwal Medhi$^1$, Helen K. Saikia
$^1$Department of Mathematics
Girijananda Chowdhury Institute of Management and Technology
Guwahati, 781017, INDIA
$^2$Department of Mathematics
Gauhati University
Guwahati, 781014, INDIA


Abstract. In this paper our attempt is to extend the notion of essential fuzzy ideals of rings to T-fuzzy essential ideals. Various properties on T-fuzzy essential ideals are established. Some results are being discussed which establish necessary and sufficient condition between T-fuzzy essential ideal in fuzzy set theory and essential ideal in crisp set theory. Moreover it is proved that if $\mu, \nu$ and $\sigma$ are non-zero T-fuzzy left ideals of $R$ such that $\mu\subseteq\nu\subseteq\sigma$, then $\mu\subseteq_{e(T)}\sigma$ if and only if $\mu\subseteq_{e(T)}\nu\subseteq_{e(T)}\sigma$.

Received: May 27, 2013

AMS Subject Classification: 03E72

Key Words and Phrases: essential fuzzy ideal, T-fuzzy essential ideal

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DOI: 10.12732/ijpam.v89i3.5 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 3