Noor, A. S. A.; Akhter, Nasima Homomorphism kernels and standard ideals of a nearlattice. (English) Zbl 1107.06005 Southeast Asian Bull. Math. 29, No. 6, 1101-1106 (2005). Summary: We show that, in a nearlattice, if join and meet of an arbitrary ideal \(I\) with a standard ideal are principal, then \(I\) itself is principal. Then we show that, in a sectionally complemented nearlattice, every congruence is a standard congruence. We also show that, in a relatively complemented nearlattice with 0, the congruence lattice is Boolean if every standard ideal is generated by a finite number of standard elements. MSC: 06A12 Semilattices 06B10 Lattice ideals, congruence relations Keywords:principal ideal; nearlattice homomorphism; homomorphism kernel; sectionally complemented nearlattice; congruence; relatively complemented nearlattice PDFBibTeX XMLCite \textit{A. S. A. Noor} and \textit{N. Akhter}, Southeast Asian Bull. Math. 29, No. 6, 1101--1106 (2005; Zbl 1107.06005)