<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It is indicated that the axioms of a Sheffer stroke BCK-algebra are independent. The relationship between a Sheffer stroke BCK-algebra and a BCK-algebra is stated. After describing a commutative, an implicative and an involutory Sheffer stroke BCK-algebras, some of important properties are proved. The relationship of this structures is demonstrated. A Sheffer stroke BCK-algebra with condition (S) is described and the connection with other structures is shown. Finally, it is proved that for a Sheffer stroke BCK-algebra to be a Boolean lattice, it must be an implicative Sheffer stroke BCK-algebra.</p>
</abstract>

In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It is indicated that the axioms of a Sheffer stroke BCK-algebra are independent. The relationship between a Sheffer stroke BCK-algebra and a BCK-algebra is stated. After describing a commutative, an implicative and an involutory Sheffer stroke BCK-algebras, some of important properties are proved. The relationship of this structures is demonstrated. A Sheffer stroke BCK-algebra with condition (S) is described and the connection with other structures is shown. Finally, it is proved that for a Sheffer stroke BCK-algebra to be a Boolean lattice, it must be an implicative Sheffer stroke BCK-algebra.

Class of Sheffer stroke BCK-algebras

Faculty of Mathematics and Computer Shahid Bahonar University of Kerman

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Class of Sheffer stroke BCK-algebras"}

In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It is indicated that the axioms of a Sheffer stroke BCK-algebra are...

Class of Sheffer stroke BCK-algebras

Published Online: Mar 12, 2022

Page range: 247 - 269

Received: Apr 27, 2021

Accepted: Jul 31, 2021

DOI: https://doi.org/10.2478/auom-2022-0014

Keywords
(Sheffer stroke) BCK-algebra, (implicative, bounded, involutory, positive implicative, commutative) Sheffer stroke BCK-algebra, BCK-lattice

© 2022 Tahsin Oner et al., published by Sciendo

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

Class of Sheffer stroke BCK-algebras

Published Online: Mar 12, 2022

Page range: 247 - 269

Received: Apr 27, 2021

Accepted: Jul 31, 2021

DOI: https://doi.org/10.2478/auom-2022-0014

Keywords(Sheffer stroke) BCK-algebra, (implicative, bounded, involutory, positive implicative, commutative) Sheffer stroke BCK-algebra, BCK-lattice

© 2022 Tahsin Oner et al., published by Sciendo

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

Keywords
(Sheffer stroke) BCK-algebra, (implicative, bounded, involutory, positive implicative, commutative) Sheffer stroke BCK-algebra, BCK-lattice