Boolean filters in pseudo-complemented almost distributive lattices

N. Rafi; Ravi Kumar Bandaru; G.C. Rao

Discussiones Mathematicae - General Algebra and Applications (2015)

  • Volume: 35, Issue: 2, page 119-128
  • ISSN: 1509-9415

Abstract

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In this paper we have introduced the concept of Boolean filters in a pseudo-complemented Almost Distributive Lattice (pseudo-complemented ADL) and studied their properties. Finally, a Boolean filter is characterized in terms of filter congruences.

How to cite

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N. Rafi, Ravi Kumar Bandaru, and G.C. Rao. "Boolean filters in pseudo-complemented almost distributive lattices." Discussiones Mathematicae - General Algebra and Applications 35.2 (2015): 119-128. <http://eudml.org/doc/276683>.

@article{N2015,
abstract = {In this paper we have introduced the concept of Boolean filters in a pseudo-complemented Almost Distributive Lattice (pseudo-complemented ADL) and studied their properties. Finally, a Boolean filter is characterized in terms of filter congruences.},
author = {N. Rafi, Ravi Kumar Bandaru, G.C. Rao},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {Almost Distributive Lattice (ADL); pseudo-complemented ADL; Boolean filter; maximal filter; congruence; Boolean algebra},
language = {eng},
number = {2},
pages = {119-128},
title = {Boolean filters in pseudo-complemented almost distributive lattices},
url = {http://eudml.org/doc/276683},
volume = {35},
year = {2015},
}

TY - JOUR
AU - N. Rafi
AU - Ravi Kumar Bandaru
AU - G.C. Rao
TI - Boolean filters in pseudo-complemented almost distributive lattices
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2015
VL - 35
IS - 2
SP - 119
EP - 128
AB - In this paper we have introduced the concept of Boolean filters in a pseudo-complemented Almost Distributive Lattice (pseudo-complemented ADL) and studied their properties. Finally, a Boolean filter is characterized in terms of filter congruences.
LA - eng
KW - Almost Distributive Lattice (ADL); pseudo-complemented ADL; Boolean filter; maximal filter; congruence; Boolean algebra
UR - http://eudml.org/doc/276683
ER -

References

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  1. [1] G. Birkhoff, Lattice Theory (Amer. Math. Soc. Colloq. Publ. XXV, Providence, 1967), USA. 
  2. [2] G. Gratzer, General Lattice Theory (Academic Press, New York, San Fransisco, 1978). Zbl0436.06001
  3. [3] G.C. Rao, Almost Distributive Lattices (Doctoral Thesis, 1980), Department of Mathematics, Andhra University, Visakhapatnam. 
  4. [4] M. Sambasiva Rao and K.P. Shum, Boolean filters of distributive lattices, International Journal of Mathematics and Soft Computing 3 (3) (2013), 41-48. 
  5. [5] U.M. Swamy and G.C. Rao, Almost distributive lattices, J. Aust. Math. Soc. (Series A) 31 (1981), 77-91. doi: 10.1017/s1446788700018498 Zbl0473.06008
  6. [6] U.M. Swamy, G.C. Rao and G. Nanaji Rao, Pseudo-complementation on almost distributive lattices, Southeast Asian Bullettin of Mathematics 24 (2000), 95-104. doi: 10.1007/s10012-000-0095-5 Zbl0982.06011

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