Geodesic
On JP-semilattices of Begum and Noor
Mathematica Bohemica, Tome 138 (2013) no. 2, pp. 181-184

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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.
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.
DOI : 10.21136/MB.2013.143290
Classification : 06A12, 06B75, 08A55
Keywords: JP-semilattice; meet semilattice; nearlattice; partial lattice 
Cīrulis, Jānis. On JP-semilattices of Begum and Noor. Mathematica Bohemica, Tome 138 (2013) no. 2, pp. 181-184. doi: 10.21136/MB.2013.143290
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