D-Effect Algebra can Be Made into a D-Total Algebra
Mathematics Letters
Volume 3, Issue 6, December 2017, Pages: 71-76
Received: Apr. 11, 2017; Accepted: May 20, 2017; Published: Nov. 28, 2017
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Authors
Ahmed Allam, Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Nabila Mikhaeel, Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Huda Merdach, Department of Mathematics, Faculty of Science, Damietta University, Damietta, Egypt
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Abstract
In this paper we prove that every D-effect algebra (E, ∆, 0, 1) can be made into a D-total algebra (E, ⍍, ¬, 1) in such a way that two elements are compatible in (E, ∆, 0, 1) if and only if they commute in(E, ⍍, ¬, 1) where x ∆ y =(x' + y')'.
Keywords
D-Basic Algebra, Weak D-Basic Algebra, Antitone Involution, D-Effect Algebra, D-Total Algebra
To cite this article
Ahmed Allam, Nabila Mikhaeel, Huda Merdach, D-Effect Algebra can Be Made into a D-Total Algebra, Mathematics Letters. Vol. 3, No. 6, 2017, pp. 71-76. doi: 10.11648/j.ml.20170306.13
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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