Janis Cirulis, University of Latvia, Riga, Latvia, e-mail: jc@lanet.lv
Abstract: In recent papers, S. N. Begum and A. S. A. Noor have studied join partial semilattices (JP-semilattices) defined as meet semilattices with an additional partial operation (join) satisfying certain axioms. We show why their axiom system is too weak to be a satisfactory basis for the authors' constructions and proofs, and suggest an additional axiom for these algebras. We also briefly compare axioms of JP-semilattices with those of nearlattices, another kind of meet semilattices with a partial join operation.
Keywords: JP-semilattice, meet semilattice, nearlattice, partial lattice
Classification (MSC 2010): 06A12, 06B75, 08A55
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