MODULAR AND STRONGLY DISTRIBUTIVE ELEMENTS IN A NEAR LATTICE

admin May 15, 2015

Authors:

Md. Zaidur Rahman ,A. S. A. Noor,

DOI NO:

https://doi.org/10.26782/jmcms.2012.07.00005

Keywords:

modular elements,nearlattice,strongly distributive elements,

Abstract

n this paper the authors have introduced the notion of modular elements in a nearlattice. We have included several characterizations of modular and strongly distributive elements with examples. We have also proved that an element in a nearlattice is standard if and only if it is both modular and strongly distributive.

Refference:

I.W. H. Cornosh and A. S. A. Noor; Standard elements in a nearlattice, Bull. Austral. Math .Soc. 26(2), (1982); 185-213.

II.G. Gratzer and E.T. Schmidt, Standrad ideals in lattices, Acta. Math. Acad. Sci. Hung. 12(1961); 17-86.

III.A. S. A Noor and A. K. M. S. Islam, Relative annihilators in nearlattices, The Rajshahi University Studies (part-B) 25(1997); 117-120.

IV.M. R. Talukder and A. S. A. Noor, Modular ideals of a join semilattice Directed below, SEA Bull. Math 22(1998); 215-218.

V.M. B. Rahman, A study on distributive nearlattices, Ph.D Thesis, Rajshahi University, Bangladesh, (1994)

Md. Zaidur Rahman , A. S. A. Noor View Download