Principal <i>n</i>-Ideals which Form Generalized Stone Nearlattices
Keywords:Principal n-ideal, Minimal prime n-ideal, Central element, Generalized Stone nearlattice.
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.
J. Sci. Res. 6 (2), 233-241 (2014)
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