| Title:
|
Congruence kernels of distributive PJP-semilattices (English) |
| Author:
|
Begum, S. N. |
| Author:
|
Noor, A. S. A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
225-239 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices. (English) |
| Keyword:
|
semilattice |
| Keyword:
|
distributivity |
| Keyword:
|
pseudocomplementation |
| Keyword:
|
congruence |
| Keyword:
|
kernel ideal |
| Keyword:
|
cokernel |
| MSC:
|
06A12 |
| MSC:
|
06B10 |
| MSC:
|
06B99 |
| MSC:
|
06D15 |
| idZBL:
|
Zbl 1249.06004 |
| idMR:
|
MR2893973 |
| DOI:
|
10.21136/MB.2011.141645 |
| . |
| Date available:
|
2011-09-22T14:54:17Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141645 |
| . |
| Reference:
|
[1] Begum, S. N., Noor, A. S. A.: Some characterizations of modular and distributive JP-semilattices.Submitted. |
| Reference:
|
[2] Blyth, T. S.: Ideals and filters of pseudo-complemented semilattices.Proc. Edinb. Math. Soc., II. Ser. 23 (1980), 301-316. Zbl 0484.06004, MR 0620927, 10.1017/S0013091500003850 |
| Reference:
|
[3] Chajda, I., Kolařík, M.: Ideals, congruences and annihilators on nearlattices.Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Math. 45 (2006), 43-52. MR 2321296 |
| Reference:
|
[4] Chajda, I., Kolařík, M.: A decomposition of homomorphic images of near lattices.Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Math. 45 (2006), 43-52. MR 2321296 |
| Reference:
|
[5] Chajda, I., Kolařík, M.: Nearlattices.Discrete Math. 308 (2008), 4906-4913. Zbl 1151.06004, MR 2446101, 10.1016/j.disc.2007.09.009 |
| Reference:
|
[6] Cornish, W. H.: Congruence on distributive pseudo-complemented lattices.Bull. Austral. Math. Soc. 82 (1973), 161-179. MR 0318024, 10.1017/S0004972700042404 |
| Reference:
|
[7] Cornish, W. H., Hickman, R. C.: Weakly distributive semilattices.Acta Math. Acad. Sci. Hungar. 32 (1978), 5-16. Zbl 0497.06005, MR 0551490, 10.1007/BF01902195 |
| Reference:
|
[8] Cornish, W. H., Noor, A. S. A.: Standard elements in a nearlattice.Bull. Austral. Math. Soc. 26 (1982), 185-213. Zbl 0523.06006, MR 0683652, 10.1017/S0004972700005700 |
| Reference:
|
[9] Grätzer, G.: Lattice Theory: First Concepts and Distributive Lattices.Freeman (1971). MR 0321817 |
| Reference:
|
[10] Grätzer, G.: General Lattice Theory.Birkhäuser (1978). MR 0504338 |
| Reference:
|
[11] Hickman, R. C.: Distributivity in Semilattices.Ph.D. Thesis, The Flinders University of South Australia (1978). Zbl 0389.06003, MR 0551491 |
| Reference:
|
[12] Noor, A. S. A., Cornish, W. H.: Multipliers on a nearlattice.Comment Math. Univ. Carolin. 27 (1986), 815-827. Zbl 0605.06005, MR 0874675 |
| Reference:
|
[13] Murty, P. V. Ramana, Rao, V. V. Rama: Characterization of certain classes of pseudo complemented semi-lattices.Algebra Universalis 4 (1974), 289-300. MR 0366763, 10.1007/BF02485741 |
| . |
