Principal <i>n</i>-Ideals which Form Generalized Stone Nearlattices

Authors

  • Shiuly Akhter University of Rajshahi
  • A.S.A Noor East-West University

DOI:

https://doi.org/10.3329/jsr.v6i2.10818

Keywords:

Principal n-ideal, Minimal prime n-ideal, Central element, Generalized Stone nearlattice.

Abstract

In this paper, we give several characterizations of those  Pn(S) which are generalized Stone nearlattices in terms of n-ideals. We show that when n is a central element of a nearlattice S and Pn(S) is a sectionally pseudocomplemented distributive nearlattice, then Pn(S) is generalized Stone if and only if for any x?S, <x>n+ V <x>n++ = S. Moreover, when Pn(S) is sectionally pseudocomplemented distributive nearlattice, then we prove that Pn(S) is generalized Stone if and only if each prime n-ideal contains a unique minimal prime n-ideal.

Keywords: Principal n-ideal; Minimal prime n-ideal; Central element; Generalized Stone nearlattice.

© 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

doi: http://dx.doi.org/10.3329/jsr.v6i2.10818

J. Sci. Res. 6 (2), 233-241 (2014)

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Author Biographies

Shiuly Akhter, University of Rajshahi

Dept. of Maths

Assistant Professor

A.S.A Noor, East-West University

Department of ECE and Professor

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Published

2014-04-23

How to Cite

Akhter, S., & Noor, A. (2014). Principal <i>n</i>-Ideals which Form Generalized Stone Nearlattices. Journal of Scientific Research, 6(2), 233–241. https://doi.org/10.3329/jsr.v6i2.10818

Issue

Vol. 6 No. 2 (2014)

Section

Section A: Physical and Mathematical Sciences

License

© Journal of Scientific Research

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