On JP-semilattices of Begum and Noor. (English) Zbl 1289.06003

Cīrulis, Jānis

Math. Bohem. 138, No. 2, 181-184 (2013).

In recent papers [“Some characterizations of modular and distributive JP-semilattices”, Atl. Electron. J. Math. 4, 56–69 (2011); Math. Bohem. 136, No. 3, 225–239 (2011; Zbl 1249.06004)], S. N. Begum and A. S. A. Noor studied join partial semilattices (JP-semilattices) defined as meet semilattices with an additional partial operation (join) satisfying certain axioms. The author shows that their axiom system is too weak to be a satisfactory basis for their constructions and proofs. Also, he improves the definition of a JP-semilattice in order to ensure the validity of their announced results.

Reviewer: Jan Paseka (Brno)

MSC:

06A12	Semilattices
06B75	Generalizations of lattices
08A55	Partial algebras

Keywords:

JP-semilattice; meet semilattice; nearlattice; partial lattice

Citations:

Zbl 1249.06004