MATHEMATICA BOHEMICA, Vol. 138, No. 2, pp. 181-184, 2013

On JP-semilattices of Begum and Noor

Janis Cirulis

Janis Cirulis, University of Latvia, Riga, Latvia, e-mail:

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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