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Keywords:
JP-semilattice; meet semilattice; nearlattice; partial lattice
JP-semilattice; meet semilattice; nearlattice; partial lattice
Summary:
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.
References:
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[2] Begum, S. N., Noor, A. S. A.: Congruence kernels of distributive PJP-semilattices. Math. Bohem. 136 (2011), 225-239. MR 2893973 | Zbl 1249.06004
[3] Chajda, I., Seidl, Z.: An algebraic approach to partial lattices. Demonstr. Math. 30 (1997), 485-494. MR 1601809 | Zbl 0910.06006
[4] Cīrulis, J.: Subtractive nearsemilattices. Proc. Latv. Acad. Sci., Sect. B, Nat. Exact Appl. Sci. 52 (1998), 228-233. MR 1788173 | Zbl 1027.06007
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