On Semi Prime Ideals in Lattices

admin May 16, 2015

Authors:

R. M. Hafizur Rahman,M. Ayub Ali ,A. S. A. Noor ,

DOI NO:

https://doi.org/10.26782/jmcms.2013.01.00006

Keywords:

semi-prime ideals,0-distributive lattices,annihilator ideals,

Abstract

Recently Yehuda Rav has given the concept of Semi-prime ideals in a general lattice by generalizing the notion of 0-distributive lattices. In this paper we study several properties of these ideals and include some of their characterizations. We give some results regarding maximal filters and include a number of Separation properties in a general lattice with respect to the annihilator ideals containing a semi-prime ideal.

Refference:

I. Balasubramani P. and Venkatanarasimhan P.V., Characterizations of the 0-Distributive Lattices, Indian J. pure appl.Math. 32(3) 315-324, (2001).

II. Powar Y.S. and Thakare N. K., 0-Distributive semilattices, Canad. Math. Bull. Vol.21(4) (1978), 469-475.

III. Rav Y., Semi prime ideals in general lattices, Journal of pure and Applied Algebra, 56(1989) 105- 118.

IV. Varlet J. C., A generalization of the notion of pseudo-complementedness, Bull. Soc. Sci. Liege, 37(1968), 149-158.

R. M. Hafizur Rahman, M. Ayub Ali ,A. S. A. Noor View Download