Principal n-Ideals which Form Generalized Stone Nearlattices - Akhter, Shiuly; Noor, A.S.A (Journal of Scientific Research, 2014)
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)