INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND - Volume 6, Issue 8, December 2017

Pages: 1-9
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n - NORMAL ALMOST DISTRIBUTIVE LATTICES

Author: S. RAVI KUMAR and G.C. RAO

Category: Engineering, Science and Mathematics

Abstract:

The concept of n-normal lattices was introduced by William H. Cornish[7]. We defined an n-prime ideal in an ADL R and characterized an n - prime ideal in terms of distinct prime ideals of R. An n-normal ADL is defined and it is proved that an ADL R is an n-normal ADL if and only if for each prime ideal P of R, is an n+1 prime ideal of R. Also, we characterized an n-normal ADL in terms of its minimal prime ideals and also in terms of its annihilators. A sectionally n-normal ADL is defined in a natural way and it is proved that an ADL R is n-normal if and only if R is sectionally n-normal. Finally, it is proved that every ideal in an ADL R is n-normal as a sub ADL of R if and only if R is n-normal.

Keywords: Almost Distributive Lattice(ADL), n-prime ideal, n-Normal ADL.