On JP-semilattices of Begum and Noor
Mathematica Bohemica (2013)
- Volume: 138, Issue: 2, page 181-184
- ISSN: 0862-7959
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topCīrulis, Jānis. "On JP-semilattices of Begum and Noor." Mathematica Bohemica 138.2 (2013): 181-184. <http://eudml.org/doc/252480>.
@article{Cīrulis2013,
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.},
author = {Cīrulis, Jānis},
journal = {Mathematica Bohemica},
keywords = {JP-semilattice; meet semilattice; nearlattice; partial lattice; JP-semilattice; meet semilattice; nearlattice; partial lattice},
language = {eng},
number = {2},
pages = {181-184},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On JP-semilattices of Begum and Noor},
url = {http://eudml.org/doc/252480},
volume = {138},
year = {2013},
}
TY - JOUR
AU - Cīrulis, Jānis
TI - On JP-semilattices of Begum and Noor
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 2
SP - 181
EP - 184
AB - 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.
LA - eng
KW - JP-semilattice; meet semilattice; nearlattice; partial lattice; JP-semilattice; meet semilattice; nearlattice; partial lattice
UR - http://eudml.org/doc/252480
ER -
References
top- Begum, S. N., Noor, A. S. A., Some characterizations of modular and distributive JP-semilattices, Atl. Electron. J. Math. 4 (2011), 56-69. (2011) MR2900988
- Begum, S. N., Noor, A. S. A., Congruence kernels of distributive PJP-semilattices, Math. Bohem. 136 (2011), 225-239. (2011) Zbl1249.06004MR2893973
- Chajda, I., Seidl, Z., An algebraic approach to partial lattices, Demonstr. Math. 30 (1997), 485-494. (1997) Zbl0910.06006MR1601809
- Cīrulis, J., Subtractive nearsemilattices, Proc. Latv. Acad. Sci., Sect. B, Nat. Exact Appl. Sci. 52 (1998), 228-233. (1998) Zbl1027.06007MR1788173
- Cīrulis, J., 10.2478/s11533-007-0008-2, Centr. Eur. J. Math. 5 (2007), 264-279. (2007) Zbl1125.03047MR2300273DOI10.2478/s11533-007-0008-2
- al., G. Grätzer et, General Lattice Theory. Second edition, Birkhäuser, Basel (1998). (1998) MR1670580
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