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Title: On JP-semilattices of Begum and Noor (English)
Author: Cīrulis, Jānis
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 138
Issue: 2
Year: 2013
Pages: 181-184
Summary lang: English
Category: math
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. (English)
Keyword: JP-semilattice
Keyword: meet semilattice
Keyword: nearlattice
Keyword: partial lattice
MSC: 06A12
MSC: 06B75
MSC: 08A55
idZBL: Zbl 06221248
idMR: MR3112364
DOI: 10.21136/MB.2013.143290
Date available: 2013-05-27T14:26:23Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] Begum, S. N., Noor, A. S. A.: Some characterizations of modular and distributive JP-semilattices.Atl. Electron. J. Math. 4 (2011), 56-69. MR 2900988
Reference: [2] Begum, S. N., Noor, A. S. A.: Congruence kernels of distributive PJP-semilattices.Math. Bohem. 136 (2011), 225-239. Zbl 1249.06004, MR 2893973
Reference: [3] Chajda, I., Seidl, Z.: An algebraic approach to partial lattices.Demonstr. Math. 30 (1997), 485-494. Zbl 0910.06006, MR 1601809
Reference: [4] Cīrulis, J.: Subtractive nearsemilattices.Proc. Latv. Acad. Sci., Sect. B, Nat. Exact Appl. Sci. 52 (1998), 228-233. Zbl 1027.06007, MR 1788173
Reference: [5] Cīrulis, J.: Hilbert algebras as implicative partial semilattices.Centr. Eur. J. Math. 5 (2007), 264-279. Zbl 1125.03047, MR 2300273, 10.2478/s11533-007-0008-2
Reference: [6] al., G. Grätzer et: General Lattice Theory. Second edition.Birkhäuser, Basel (1998). MR 1670580


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