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On properties of the free BCI-algebra with one generator

  • Alfonz Haviar EMAIL logo and Pavol Konôpka
Published/Copyright: November 3, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 4

Abstract

In this paper we show that the free BCI-algebra with one generator has an infinite number of branches and that every branch (as a poset) has the least and the greatest element and is of infinite length and width.

MSC 2010: Primary 06F35
keywords: BCI-algebra; free BCI-algebra

(Communicated by Miroslav Ploščica)

Acknowledgement

The authors would like to thank the referee for many valuable suggestions.

References

[1] Huang Yisheng: BCI-Algebra, Science Press, Bejiing, 2006.Search in Google Scholar

[2] Kashima, K.–Komori, K.: The word problem for free BCI-algebras is decidable, Math. Japonica 37 (1992), 1025–1029.Search in Google Scholar

[3] Raftery, J. G.–Van Alten, C. J.: Residuation in commutative ordered monoids with minimal zero, Rep. Math. Logic 34 (2000), 23–57.Search in Google Scholar

Received: 2012-12-10
Accepted: 2014-2-27
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0180
Keywords for this article
BCI-algebra; free BCI-algebra

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  4. An approach to orthomodular lattices via lattices with an antitone involution
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  13. Research Article
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