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ArticleOriginal scientific text

Title

An equational axiomatization of Post Almost Distributive Lattices

Authors 1, 2

Affiliations

  1. Department of Mathematics, K.B.N. Degree and P.G.College, Vijayawada – 520001
  2. Institute of Mathematics, Yunnan University, Kunming 650091, China

Abstract

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

Keywords

ENG
Almost Distributive Lattices (ADL), P₂-algebras, P₂-Almost Distributive Lattices (P₂-ADL), Post algebras, Post Almost Distributive Lattices (Post ADL)

Bibliography

  1. G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ. XXV, Providence (1967), USA.
  2. G. Epstein and A. Horn, P-algebras, an abstraction from Post algebras, Algebra Universalis 4 (1) (1974), 195-206.
  3. G. Epstein and A. Horn, Chain based Lattices, Pacific J. Math. 55 (1) (1974), 65-84.
  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.
  5. G.C. Rao and A. Berhanu, Heyting almost distributive lattices, Inter. Jour. Comp. Cogn. 8 (3) (2010), 85-89.
  6. G.C. Rao and A. Mihret, P₀-almost distributive lattices, to appear in Southeast Asian Bull. Math.
  7. G.C. Rao and A. Mihret, P₂-almost distributive lattices, accepted for publication in Journal of Global research in Mathematical Archives.
  8. G.C. Rao and A. Mihret, Post almost distributive lattices, Accepted for publication in Southeast Asian Bull. Math.
  9. G.C. Rao, A. Mihret and Naveen Kumar Kakumanu, P₁-almost distributive lattices, Inter. J. Math. Archive 4 (2) (2013), 100-110.
  10. G.C. Rao and Naveen Kumar Kakumanu, B-almost distributive lattices, Southeast Asian Bulletin of Mathematics 39 (2015), 545-554.
  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
  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
  13. Naveen Kumar Kakumanu, Notes on post almost distributive lattices, communicated for publication.
  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. G.C. Rao and Naveen Kumar Kakumanu, Pseudo-supplemented almost distributive lattices, Southeast Asian Bull. Math. 37 (2013), 131-138.
  16. U.M. Swamy and G.C. Rao, Almost distributive lattices, J. Aust. Math. Soc. (A) 31 (1981), 77-91.
  17. U.M. Swamy and S. Ramesh, Birkhoff center of ADL, Int. J. Algebra 3 (2009), 539-546.
Discussiones Mathematicae - General Algebra and Applications
2016/36/1
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Pages:
5-13
Main language of publication
English
Received
2014-10-22
Accepted
2016-03-11
Published
2016

DOI: 10.7151/dmgaa.1246

Exact and natural sciences