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Homomorphism kernels and standard ideals of a nearlattice. (English) Zbl 1107.06005

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
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