On generalized Hilbert algebras

Authors

  • R.A. Borzooei University of Shahid Beheshti - Department of Mathematics
  • J. Shohani Sistan and Balushestan University . Department of Mathematics

Keywords:

generalized Hilbert algebra, implication algebras, complemented lattice, distributive lattice, Boolean algebra

Abstract

In this paper by considering the notion of generalized Hilbert algebra which is named g-Hilbert algebra, we obtain some properties of it.  Moreover, we show that for all n ≥ 3 there exist at least one proper g-Hilbert algebra of order n.  Becaus g-Hilbert algebra is not a Boolean algebra we define the concept of branch in g-Hilbert algebras and we prove that any branch in commutative g-Hilbert algebras is a Boolean algebra.

Cover of n°29 Italian Journal of Pure and Applied Mathematics

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Published

2012-12-11

How to Cite

Borzooei, R., & Shohani , J. (2012). On generalized Hilbert algebras. Italian Journal of Pure and Applied Mathematics, 29, 71–86. Retrieved from https://journals.uniurb.it/index.php/ijpam/article/view/6059

Issue

N°29 - December 2012

Section

Articoli - Forum Editrice

License

Copyright (c) 2012 R.A. Borzooei, J. Shohani

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

L'opera è pubblicata sotto  Licenza Creative Commons Attribuzione 4.0 Internazionale (CC-BY)

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