| 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:
|
http://hdl.handle.net/10338.dmlcz/143290 |
| . |
| 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 |
| . |
