Joshi, Vinayak On completion of section semicomplemented posets. (English) Zbl 1150.06001 Southeast Asian Bull. Math. 31, No. 5, 881-892 (2007). Summary: In this paper, we prove that the completion by cuts of a section semicomplemented (in brief SSC) poset is section semicomplemented. It is shown that a finite distributive section semicomplemented poset need not be Boolean. However, its completion by cuts is a Boolean lattice. The concepts of normal ideals and subprojective ideals are introduced in posets and it is proved that the center of the completion by cuts of a section semicomplemented and dually section semicomplemented poset \(P\) is precisely the set of normal subprojective ideals of \(P\). Further, it is proved that in an SSC and SSC\(^*\) (the dual of SSC) poset \(P\), a principal ideal \(J_s\) is subprojective if and only if \(s\) is a neutral element of \(P\). Cited in 5 Documents MSC: 06A06 Partial orders, general 06C15 Complemented lattices, orthocomplemented lattices and posets Keywords:semicomplements; posets; distributive posets; normal ideals; subprojective ideals PDFBibTeX XMLCite \textit{V. Joshi}, Southeast Asian Bull. Math. 31, No. 5, 881--892 (2007; Zbl 1150.06001)