Some Results on Normal meet Semilattices

Authors:

Momtaz Begum,A.S.A.Noor,

DOI NO:

https://doi.org/10.26782/jmcms.2014.07.00004

Keywords:

normal semilattices,0-distributivity, ideals,meet semilattices,

Abstract

In this paper we introduce the concept of normal semilattices in presence of 0-distributivity and include a nice characterization of normal semilattices. We also study the p-ideals in pseudo complemented meet semilattices. Then we give the notion of S-semilattices and prove that every S-semilattice is comaximal, although its converse in not true. Finally, we prove that every S-semilattice is normal, but the converse need not be true.

Refference:

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

II. H.S.Chakraborty and M.R.Talukder, Some characterizations of 0-distributive semilattices, Accepted in the Bulletin of Malaysian Math. Sci.Soc.

III. Cornish, W.H. Normal lattices, J. Austral Math. Soc. 14 (1972), 200-215.

IV. R.M. Hafizur Rahizur Rahman, M. Ayub Ali and A.S.A . Noor, On semi prime ideals in lattices, ISSN 0973-8975, J. Mech. Cont. & Math. Sci., Vol.-7, No.-2, January (2013) Pages 1094-1102.

V.Momtaz Begum and A.S.A. Noor, Semi prime ideals in meet semilattices, Annals of Pure & appl.Math.Vol.1, No.2, 2012, 149-157. Nag , C. Begum S.N. and Taluhder, M.R. Some characterizations of subclasses of P-algebras. Manuscript.

VI. A.S.A. Noor and Momtaz Begum, Some Properties of 0-distributive Meet Semilattices, Annals of Pure & appl. Math.Vol.2, No.1, 2012, 60-66.

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

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

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

Author(s) : Momtaz Begum and A.S.A.Noor View Download