Class of Sheffer stroke BCK-algebras

Tahsin Oner; Tugce Kalkan; Arsham Borumand Saeid

doi:10.2478/auom-2022-0014

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Class of Sheffer stroke BCK-algebras

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 30 (2022): Issue 1 (February 2022)

By: Tahsin Oner, Tugce Kalkan and Arsham Borumand Saeid

Open Access

|Mar 2022

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.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2022-0014 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 247 - 269

Submitted on: Apr 27, 2021

Accepted on: Jul 31, 2021

Published on: Mar 12, 2022

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

(Sheffer stroke) BCK-algebra,

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

BCK-lattice

Related subjects:

Mathematics,

General mathematics

© 2022 Tahsin Oner, Tugce Kalkan, Arsham Borumand Saeid, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 30 (2022): Issue 1 (February 2022)