<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The main goal of this paper is to give some representations of MV-algebras in terms of derivations. In this paper, we investigate some properties of implicative and difference derivations and give their characterizations in MV-algebras. Then, we show that every Boolean algebra (idempotent MV-algebra) is isomorphic to the algebra of all implicative derivations and obtain that a direct product representation of MV-algebra by implicative derivations. Moreover, we prove that regular implicative and difference derivations on MV-algebras are in one to one correspondence and show that the relationship between the regular derivation pair (<italic>d, g</italic>) and the Galois connection, where <italic>d</italic> and <italic>g</italic> are regular difference and implicative derivation on <italic>L</italic>, respectively. Finally, we obtain that regular difference derivations coincide with direct product decompositions of MV-algebras.</p></abstract>

The main goal of this paper is to give some representations of MV-algebras in terms of derivations. In this paper, we investigate some properties of implicative and difference derivations and give their characterizations in MV-algebras. Then, we show that every Boolean algebra (idempotent MV-algebra) is isomorphic to the algebra of all implicative derivations and obtain that a direct product representation of MV-algebra by implicative derivations. Moreover, we prove that regular implicative and difference derivations on MV-algebras are in one to one correspondence and show that the relationship between the regular derivation pair (d, g) and the Galois connection, where d and g are regular difference and implicative derivation on L, respectively. Finally, we obtain that regular difference derivations coincide with direct product decompositions of MV-algebras.

Study of MV-algebras via derivations

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Study of MV-algebras via derivations"}

The main goal of this paper is to give some representations of MV-algebras in terms of derivations. In this paper, we investigate some properties of...

Study of MV-algebras via derivations

Published Online: Dec 21, 2019

Page range: 259 - 278

Received: Dec 05, 2018

Accepted: Mar 31, 2019

DOI: https://doi.org/10.2478/auom-2019-0044

Keywords
MV-algebra, implicative derivation, difference derivation, Boolean algebra

© 2019 Jun Tao Wang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Study of MV-algebras via derivations

Published Online: Dec 21, 2019

Page range: 259 - 278

Received: Dec 05, 2018

Accepted: Mar 31, 2019

DOI: https://doi.org/10.2478/auom-2019-0044

KeywordsMV-algebra, implicative derivation, difference derivation, Boolean algebra

© 2019 Jun Tao Wang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
MV-algebra, implicative derivation, difference derivation, Boolean algebra