1. bookVolume 30 (2022): Issue 1 (February 2022)
Journal Details
License
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English
access type Open Access

Class of Sheffer stroke BCK-algebras

Published Online: 12 Mar 2022
Volume & Issue: Volume 30 (2022) - Issue 1 (February 2022)
Page range: 247 - 269
Received: 27 Apr 2021
Accepted: 31 Jul 2021
Journal Details
License
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English
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.

Keywords

MSC 2010

[1] Bărbăcioru, C., Positive implicative BCK-algebras, Mathematica Japonica 36, 11–59, 1967. Search in Google Scholar

[2] Chajda, I., Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis Facultas Rerum Naturalium Mathematica, 44(1), 19-23, 2008. Search in Google Scholar

[3] Chajda, I., Halaš, R., Länger, H., Operations and structures derived from non-associative MV-algebras, Soft Computing, 23(12), 3935-3944, 2019.10.1007/s00500-018-3309-4650051131123427 Search in Google Scholar

[4] Davey, B., Priestley, H., Introduction to lattices and order, Cambridge University Press, Cambridge, 1990. Search in Google Scholar

[5] Huang, Y., BCI-algebras, Science Press, 2006. Search in Google Scholar

[6] Imai, Y., Iséki, K., On axiom systems of proposional calculi, XIV. Proc. Jpn. Acad., Ser. A, Math. Sci. 42, 19–22, 1966.10.3792/pja/1195522169 Search in Google Scholar

[7] Iséki, K., Tanaka, S., An introduction to the theory of BCK-algebras, Mathematica Japonica 23 (1), 1–26, 1978. Search in Google Scholar

[8] Iséki, K., BCK-algebras with condition (S), Mathematica Japonica 24(4), 107–119, 1979. Search in Google Scholar

[9] McCune, W., et.al., Short single axioms for Boolean algebra, Journal of Automated Reasoning 29 (1), 1–16, 2002. Search in Google Scholar

[10] Meng, J., Jun, Y. B., BCK-Algebras, Kyung Moon Sa Co, Seoul, Korea, 1994. Search in Google Scholar

[11] Oner, T., Katican, T., Borumand Saeid, A., Relation Between Sheffer stroke operation and Hilbert algebras, Categories and General Algebraic Structures with Applications, 14 (1), 245–268, 2021.10.29252/cgasa.14.1.245 Search in Google Scholar

[12] Oner, T., Katican, T., Borumand Saeid, A., Fuzzy filters of Sheffer stroke Hilbert algebras, Journal of Intelligent and Fuzzy Systems, 40 (1), 759-772, 2021.10.3233/JIFS-200760 Search in Google Scholar

[13] Oner, T., Katican, T., Borumand Saeid, A., Terziler, M., Filters of strong Sheffer stroke non-associative MV-algebras, Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, 29 (1), 143-164, 2021.10.2478/auom-2021-0010 Search in Google Scholar

[14] Oner, T., Katican, T., Borumand Saeid, A., (Fuzzy) filters of Sheffer stroke BL-algebras, Kragujevac Journal of Mathematics, 47 (1), 39-55, (2023).10.1080/09720502.2021.1959999 Search in Google Scholar

[15] Oner, T., Katican, T., Borumand Saeid, A., On Sheffer stroke UP-algebras, Discussiones Mathematicae - General Algebra and Applications, (in press). Search in Google Scholar

[16] Oner, T., Kalkan T., Kircali Gursoy, N., Sheffer stroke BG-algebras, International Journal of Maps in Mathematics, 4 (1), 27–39, (2021). Search in Google Scholar

[17] Oner, T., Katican, T., Borumand Saeid, A., On Sheffer stroke BE-algebras, Discussiones Mathematicae - General Algebra and Applications, (in press). Search in Google Scholar

[18] Sheffer, H. M., A set of five independent postulates for Boolean algebras, with application to logical constants, Transactions of the American Mathematical Society, 14 (4), 481–488, (1913).10.1090/S0002-9947-1913-1500960-1 Search in Google Scholar

[19] Tanaka, S., A new class of algebras, Mathematics Seminar Notes, 3, 37–43, 1975. Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo