A note on Stone join-semilattices

Shriram Nimbhorkar; Anwari Rahemani

Open Mathematics (2011)

  • Volume: 9, Issue: 4, page 929-933
  • ISSN: 2391-5455

Abstract

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Characterizations for a pseudocomplemented modular join-semilattice with 0 and 1 and its ideal lattice to be a Stone lattice are given.

How to cite

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Shriram Nimbhorkar, and Anwari Rahemani. "A note on Stone join-semilattices." Open Mathematics 9.4 (2011): 929-933. <http://eudml.org/doc/269185>.

@article{ShriramNimbhorkar2011,
abstract = {Characterizations for a pseudocomplemented modular join-semilattice with 0 and 1 and its ideal lattice to be a Stone lattice are given.},
author = {Shriram Nimbhorkar, Anwari Rahemani},
journal = {Open Mathematics},
keywords = {Pseudocomplemented lattice; Stone lattice; Modular join-semilattice; pseudocomplemented lattice; modular join-semilattice},
language = {eng},
number = {4},
pages = {929-933},
title = {A note on Stone join-semilattices},
url = {http://eudml.org/doc/269185},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Shriram Nimbhorkar
AU - Anwari Rahemani
TI - A note on Stone join-semilattices
JO - Open Mathematics
PY - 2011
VL - 9
IS - 4
SP - 929
EP - 933
AB - Characterizations for a pseudocomplemented modular join-semilattice with 0 and 1 and its ideal lattice to be a Stone lattice are given.
LA - eng
KW - Pseudocomplemented lattice; Stone lattice; Modular join-semilattice; pseudocomplemented lattice; modular join-semilattice
UR - http://eudml.org/doc/269185
ER -

References

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  1. [1] Balbes R., Horn A., Stone lattices, Duke Math. J., 1970, 37(3), 537–545 http://dx.doi.org/10.1215/S0012-7094-70-03768-3 
  2. [2] Birkhoff G., Lattice Theory, 2nd ed., Amer. Math. Soc. Colloq. Publ., 25, American Mathematical Society, New York, 1948 
  3. [3] Frink O., Pseudo-complements in semi-lattices, Duke Math. J., 1962, 29(4), 505–514 http://dx.doi.org/10.1215/S0012-7094-62-02951-4 Zbl0114.01602
  4. [4] Grätzer G., A generalization of Stone’s representation theorem for Boolean algebras, Duke Math. J., 1963, 30(3), 469–474 http://dx.doi.org/10.1215/S0012-7094-63-03051-5 Zbl0121.26702
  5. [5] Grätzer G., Lattice Theory: First concepts and Distributive Lattices, W. H. Freemanand Co., San Francisco, 1971 Zbl0232.06001
  6. [6] Grätzer G., Schmidt E. T., On a problem of M. H. Stone, Acta Math. Acad. Sci. Hungar., 1957, 8(3–4), 455–460 http://dx.doi.org/10.1007/BF02020328 
  7. [7] Katriňák T., Mederly P., Construction of p-algebras with a modular frame, Houston J. Math., 1978, 4(1), 67–79 Zbl0381.06018
  8. [8] Stone M. H., Topological representations of distributive lattices and Brouwerian logics, Časopis Pěst. Mat. Fys., 1937, 67, 1–25 Zbl0018.00303
  9. [9] Varlet J., On the characterization of Stonelattices, Acta Sci. Math. (Szeged), 1966, 27(1–2), 81–84 
  10. [10] Venkatanarasimhan P.V., A note on modular lattices, J. Indian Math. Soc., 1966, 30, 55–59 Zbl0158.01606
  11. [11] Venkatanarasimhan P.V., Pseudo-complements in posets, Proc. Amer. Math. Soc., 1971, 28(1), 9–17 http://dx.doi.org/10.1090/S0002-9939-1971-0272687-X Zbl0218.06002

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