Characterizations of m-Normal Nearlattices in terms of Principal n-Ideals

Abstract

A convex subnearlattice of a nearlattice S containing a fixed element n?S is called an n-ideal. The n-ideal generated by a single element is called a principal n-ideal. The set of finitely generated principal n-ideals is denoted by P_n(S), which is a nearlattice. A distributive nearlattice S with 0 is called m-normal if its every prime ideal contains at most m number of minimal prime ideals. In this paper, we include several characterizations of those P_n(S) which form m-normal nearlattices. We also show that P_n(S) is m-normal if and only if for any m+1 distinct minimal prime n-ideals P_o,P_1,., P_m of S, P_o ? ? P_m = S.

DOI: http://dx.doi.org/10.3329/rujs.v38i0.16548

Rajshahi University J. of Sci. 38, 49-59 (2010)