Congruence kernels of distributive PJP-semilattices

S. N. Begum; Abu Saleh Abdun Noor

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 3, page 225-239
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Begum, S. N., and Noor, Abu Saleh Abdun. "Congruence kernels of distributive PJP-semilattices." Mathematica Bohemica 136.3 (2011): 225-239. <http://eudml.org/doc/197003>.

@article{Begum2011,
abstract = {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.},
author = {Begum, S. N., Noor, Abu Saleh Abdun},
journal = {Mathematica Bohemica},
keywords = {semilattice; distributivity; pseudocomplementation; congruence; kernel ideal; cokernel; semilattice; distributivity; pseudocomplementation; congruence; kernel ideal; cokernel},
language = {eng},
number = {3},
pages = {225-239},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Congruence kernels of distributive PJP-semilattices},
url = {http://eudml.org/doc/197003},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Begum, S. N.
AU - Noor, Abu Saleh Abdun
TI - Congruence kernels of distributive PJP-semilattices
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 3
SP - 225
EP - 239
AB - 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.
LA - eng
KW - semilattice; distributivity; pseudocomplementation; congruence; kernel ideal; cokernel; semilattice; distributivity; pseudocomplementation; congruence; kernel ideal; cokernel
UR - http://eudml.org/doc/197003
ER -

References

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  1. Begum, S. N., Noor, A. S. A., Some characterizations of modular and distributive JP-semilattices, Submitted. 
  2. Blyth, T. S., 10.1017/S0013091500003850, Proc. Edinb. Math. Soc., II. Ser. 23 (1980), 301-316. (1980) Zbl0484.06004MR0620927DOI10.1017/S0013091500003850
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  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. (2006) MR2321296
  5. Chajda, I., Kolařík, M., 10.1016/j.disc.2007.09.009, Discrete Math. 308 (2008), 4906-4913. (2008) Zbl1151.06004MR2446101DOI10.1016/j.disc.2007.09.009
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  7. Cornish, W. H., Hickman, R. C., 10.1007/BF01902195, Acta Math. Acad. Sci. Hungar. 32 (1978), 5-16. (1978) Zbl0497.06005MR0551490DOI10.1007/BF01902195
  8. Cornish, W. H., Noor, A. S. A., 10.1017/S0004972700005700, Bull. Austral. Math. Soc. 26 (1982), 185-213. (1982) Zbl0523.06006MR0683652DOI10.1017/S0004972700005700
  9. Grätzer, G., Lattice Theory: First Concepts and Distributive Lattices, Freeman (1971). (1971) MR0321817
  10. Grätzer, G., General Lattice Theory, Birkhäuser (1978). (1978) MR0504338
  11. Hickman, R. C., Distributivity in Semilattices, Ph.D. Thesis, The Flinders University of South Australia (1978). (1978) Zbl0389.06003MR0551491
  12. Noor, A. S. A., Cornish, W. H., Multipliers on a nearlattice, Comment Math. Univ. Carolin. 27 (1986), 815-827. (1986) Zbl0605.06005MR0874675
  13. Murty, P. V. Ramana, Rao, V. V. Rama, 10.1007/BF02485741, Algebra Universalis 4 (1974), 289-300. (1974) MR0366763DOI10.1007/BF02485741

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