An equational axiomatization of Post Almost Distributive Lattices

Naveen Kumar Kakumanu; Kar Ping Shum

Discussiones Mathematicae General Algebra and Applications (2016)

  • Volume: 36, Issue: 1, page 5-13
  • ISSN: 1509-9415

Abstract

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In this paper, we prove that the class of P₂-Almost Distributive Lattices and Post Almost Distributive Lattices are equationally definable.

How to cite

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Naveen Kumar Kakumanu, and Kar Ping Shum. "An equational axiomatization of Post Almost Distributive Lattices." Discussiones Mathematicae General Algebra and Applications 36.1 (2016): 5-13. <http://eudml.org/doc/286885>.

@article{NaveenKumarKakumanu2016,
abstract = {In this paper, we prove that the class of P₂-Almost Distributive Lattices and Post Almost Distributive Lattices are equationally definable.},
author = {Naveen Kumar Kakumanu, Kar Ping Shum},
journal = {Discussiones Mathematicae General Algebra and Applications},
keywords = {Almost Distributive Lattices (ADL); P₂-algebras; P₂-Almost Distributive Lattices (P₂-ADL); Post algebras; Post Almost Distributive Lattices (Post ADL)},
language = {eng},
number = {1},
pages = {5-13},
title = {An equational axiomatization of Post Almost Distributive Lattices},
url = {http://eudml.org/doc/286885},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Naveen Kumar Kakumanu
AU - Kar Ping Shum
TI - An equational axiomatization of Post Almost Distributive Lattices
JO - Discussiones Mathematicae General Algebra and Applications
PY - 2016
VL - 36
IS - 1
SP - 5
EP - 13
AB - In this paper, we prove that the class of P₂-Almost Distributive Lattices and Post Almost Distributive Lattices are equationally definable.
LA - eng
KW - Almost Distributive Lattices (ADL); P₂-algebras; P₂-Almost Distributive Lattices (P₂-ADL); Post algebras; Post Almost Distributive Lattices (Post ADL)
UR - http://eudml.org/doc/286885
ER -

References

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  1. [1] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ. XXV, Providence (1967), USA. 
  2. [2] G. Epstein and A. Horn, P-algebras, an abstraction from Post algebras, Algebra Universalis 4 (1) (1974), 195-206. Zbl0294.06010
  3. [3] G. Epstein and A. Horn, Chain based Lattices, Pacific J. Math. 55 (1) (1974), 65-84. 
  4. [4] E.L. Post, The Two-Valued Iterative Systems of Mathematical Logic, Annals of Mathematics Studies, no. 5 (Princeton University Press, Princeton, N.J., 1941), viii+122 pp. Zbl0063.06326
  5. [5] G.C. Rao and A. Berhanu, Heyting almost distributive lattices, Inter. Jour. Comp. Cogn. 8 (3) (2010), 85-89. 
  6. [6] G.C. Rao and A. Mihret, P₀-almost distributive lattices, to appear in Southeast Asian Bull. Math. Zbl1346.06009
  7. [7] G.C. Rao and A. Mihret, P₂-almost distributive lattices, accepted for publication in Journal of Global research in Mathematical Archives. 
  8. [8] G.C. Rao and A. Mihret, Post almost distributive lattices, Accepted for publication in Southeast Asian Bull. Math. 
  9. [9] G.C. Rao, A. Mihret and Naveen Kumar Kakumanu, P₁-almost distributive lattices, Inter. J. Math. Archive 4 (2) (2013), 100-110. Zbl1289.06019
  10. [10] G.C. Rao and Naveen Kumar Kakumanu, B-almost distributive lattices, Southeast Asian Bulletin of Mathematics 39 (2015), 545-554. 
  11. [11] G.C. Rao and Naveen Kumar Kakumanu, BL-almost distributive lattices, Asian European Journal of Mathematicas 5 (2) (2012), 1250022-1 to 1250022-8. doi: 10.1142/S1793557112500222 Zbl1258.06009
  12. [12] G.C. Rao and Naveen Kumar Kakumanu, Characterization of BL-almost distributive lattices, Asian-European Journal of Mathematics 8 (3) (2015), 1550041 (13 pages). doi: 10.1142/S1793557115500412 Zbl1327.06011
  13. [13] Naveen Kumar Kakumanu, Notes on post almost distributive lattices, communicated for publication. 
  14. [14] Naveen Kumar Kakumanu and G.C. Rao, Properties of P₀-almost distributive lattices, Int. J. of Scientific and Innovative Mathematical Research (IJSIMR) 2 (3) (2014), 256-261. 
  15. [15] G.C. Rao and Naveen Kumar Kakumanu, Pseudo-supplemented almost distributive lattices, Southeast Asian Bull. Math. 37 (2013), 131-138. Zbl1289.06019
  16. [16] U.M. Swamy and G.C. Rao, Almost distributive lattices, J. Aust. Math. Soc. (A) 31 (1981), 77-91. Zbl0473.06008
  17. [17] U.M. Swamy and S. Ramesh, Birkhoff center of ADL, Int. J. Algebra 3 (2009), 539-546. Zbl1187.06009

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