ON FINITELY GENERATED N-IDEALS WHICH FORM RELATIVELY STONE LATTICES

admin May 10, 2015

Authors:

M. Ayub ,A.S.A.Noor,

DOI NO:

https://doi.org/10.26782/jmcms.2011.07.00002

Keywords:

lattice,finitely generated ideals,stone lattices,

Abstract

Set of all finitely generated n-ideals of  is a lattice, denoted by .  In this paper the author has characterized those  which form relatively Stone lattices. It has been shown that  is relatively Stone if and only if  for any two incomparable prime n-ideals  and  of .

Refference:

1. Ali M. Ayub, A Study on Finitely generated n-ideals of a lattice, Ph.D Thesis, 2000.
2. Cornish W. H., Normal lattices, J. Austral. Math. Soc. 14(1972), 200-215.
3. Gratzer G., Lattice theory, First Concepts and distributive lattices, Freeman, San Francisco, 1971.
4. Latif M.A. and Noor A.S.A, n-ideals of a lattice, The Rajshahi University Studies (Part B), 22 (1994), 173-180.
5. Mandelker M., Relative annihilators in lattices, Duke Math. J. 40(1970), 377- 386.
6. Noor A. S. A. and Ali M. Ayub, Relative annihilators around a neutral element of a lattice, The Rajshahi University studies(part B), 28(2000), 141-146.
7. Noor A. S. A. and Latif M.A., Finitely generated n-ideals of a lattice, SEA Bull, Math. 22 (1998), 73-79.
8. Varlet J., Relative annihilators in semilattices, Bull. Austral. Math. Soc. 9(1973), 169- 185

M. Ayub Al,A.S.A. Noor View Download