Filters of strong Sheffer stroke non-associative MV-algebras

Tahsin Oner; Tugce Katican; Arsham Borumand Saeid; Mehmet Terziler

doi:10.2478/auom-2021-0010

.blurhash-client-img { display: none !important; }

Filters of strong Sheffer stroke non-associative MV-algebras

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 29 (2021): Issue 1 (March 2021)

By: Tahsin Oner, Tugce Katican, Arsham Borumand Saeid and Mehmet Terziler

Open Access

|Apr 2021

Abstract

In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved.

References

[1] Abbott, J. C., Implicational algebras, Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, 11(1), 3-23, 1967.
Search in Google Scholar Back to article
[2] Bailey, C. G., Prime filters in MV-Algebra II, arXiv preprint, 2009. Available at arXiv:0907.3332v1[math.RA].
Search in Google Scholar Back to article
[3] H. Banivaheb and A. Borumand Saeid, MV -modules of fractions, J. Algebra and its Applications, (2020) 2050131 (19 pages).10.1142/S0219498820501315
Search in Google Scholar Back to article
[4] Birkhoff, G., Lattice Theory, Proceedings of the American Mathematical Society, 1967.
Search in Google Scholar Back to article
[5] Botur, M., Halaš, R., Commutative basic algebras and non-assocative fuzzy logics, Arch. Math. Log. 48, 243-255, 2009.10.1007/s00153-009-0125-7
Search in Google Scholar Back to article
[6] Chajda, I., Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis Facultas Rerum Naturalium Mathematica, 44(1), 19-23, 2008.
Search in Google Scholar Back to article
[7] Chajda, I., Orthomodular semilattices, Discrete Mathematics, 307(1), 115-118, 2007.10.1016/j.disc.2006.05.040
Search in Google Scholar Back to article
[8] 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 Back to article
[9] Chajda, I., Khr, J., A non-associative generalization of MV-algebras, Math. Slov., 57, 301-312, 2007.10.2478/s12175-007-0024-5
Search in Google Scholar Back to article
[10] Chajda, I., Länger, H., Properties of non-associative MV-algebras, Math. Slov., 67, 1095-1104, 2017.10.1515/ms-2017-0035
Search in Google Scholar Back to article
[11] Chang, C. C., Algebraic analysis of many-valued logics, Transactions of the American Mathematical Society, 88, 467-490, 1958.10.1090/S0002-9947-1958-0094302-9
Search in Google Scholar Back to article
[12] Chang, C. C., A new proof of the completeness of the ukasiewicz axioms, Transactions of the American Mathematical Society, 93, 7480, 1959.10.2307/1993423
Search in Google Scholar Back to article
[13] Cignoli, R. L., d’Ottaviano, I. M. L., Mundici, G., Algebraic foundations of many-valued reasoning, Springer Science and Business Media, Dordrecht, Holland, 2000.10.1007/978-94-015-9480-6
Search in Google Scholar Back to article
[14] McCune, W., Veroff, R. Fitelson, B. Harris, K. Feist, A., Wos, L., Short single axioms for Boolean algebra, Journal of Automated Reasoning, 29(1), 1-16, 2002.10.1023/A:1020542009983
Search in Google Scholar Back to article
[15] 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 Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2021-0010 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 143 - 164

Submitted on: Apr 1, 2020

Accepted on: May 25, 2020

Published on: Apr 13, 2021

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Sheffer stroke,

(Sheffer stroke) NMV-algebra,

filter,

Related subjects:

© 2021 Tahsin Oner, Tugce Katican, Arsham Borumand Saeid, Mehmet Terziler, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 29 (2021): Issue 1 (March 2021)