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Around a neutral element in a nearlattice. (English) Zbl 0627.06008

A nearlattice is defined to be a lower semilattice having the property that any two elements possessing a common upper bound have a supremum. Several notions which have been studied earlier for lattices (e.g., standard element, neutral element) are introduced and investigated in the case of nearlattices. Next, some results of M. Kolibiar [Czech. Math. J. 6(81), 318–329 (1956; Zbl 0075.02001)] on a ternary operation in lattices are extended for nearlattices.

MSC:

06A12 Semilattices
06B10 Lattice ideals, congruence relations

Citations:

Zbl 0075.02001
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