<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper MV -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper MV -algebra. </p></abstract>

Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper MV -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper MV -algebra.

Relationship Between Hyper MV -algebras and Hyperlattices

Department of Mathematics, Shahid Beheshti University Tehran,

Department of Mathematics, Payame Noor University p.o.box 19395-3697 Tehran,

Tehran Medical Sciences Branch, Islamic Azad University Tehran,

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Relationship Between Hyper MV -algebras and Hyperlattices"}

Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any...

Relationship Between Hyper MV -algebras and Hyperlattices

Published Online: Dec 30, 2016

Page range: 75 - 94

Received: Apr 11, 2015

Accepted: Apr 26, 2016

DOI: https://doi.org/10.1515/awutm-2016-0016

Keywords
MV -algebra, hyper MV -algebra, hyperlattice

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Relationship Between Hyper MV -algebras and Hyperlattices

Published Online: Dec 30, 2016

Page range: 75 - 94

Received: Apr 11, 2015

Accepted: Apr 26, 2016

DOI: https://doi.org/10.1515/awutm-2016-0016

KeywordsMV -algebra, hyper MV -algebra, hyperlattice

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
MV -algebra, hyper MV -algebra, hyperlattice