Characterizations of those <i>P</i><sub>n</sub>(S) which are Relatively Stone Nearlattice

Authors

  • S. Akhter Department of Mathematics, University of Rajshahi, Rajshahi-6205
  • A. S. A. Noor Department of Electronics and Communication Engineering, East-West University, 45 Mohakhali, Dhaka-1212

DOI:

https://doi.org/10.3329/jsr.v4i3.10103

Keywords:

Principal n-ideal, Central element, Relatively Stone nearlattice.

Abstract

For a fixed element n of a nearlattice S, a convex subnearlattice of S containing n is called an n-ideal of S. An n-ideal generated by a single element a is called a principal n-ideal, denoted by <a>n. The set of principal n-ideals is denoted by Pn(S). A distributive nearlattice S is called relatively Stone nearlattice if each closed interval [x,y] with  is a Stone lattice. In this paper, we give several characterizations of those Pn(S) which are relatively Stone in terms of n-ideals and relative n-annihilators.

© 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

doi: http://dx.doi.org/10.3329/jsr.v4i3.10103 J. Sci. Res. 4 (3), 589-601 (2012)

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Published

2012-08-28

How to Cite

Akhter, S., & Noor, A. S. A. (2012). Characterizations of those <i>P</i><sub>n</sub>(S) which are Relatively Stone Nearlattice. Journal of Scientific Research, 4(3), 589–601. https://doi.org/10.3329/jsr.v4i3.10103

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Section

Section A: Physical and Mathematical Sciences