The characterization of Nelson algebras by Sheffer stroke

Tahsin Oner; Tugce Katican; Arsham Borumand Saeid

doi:10.2478/auom-2025-0030

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

The characterization of Nelson algebras by Sheffer stroke

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 33 (2025): Issue 3 (October 2025)

By: Tahsin Oner, Tugce Katican and Arsham Borumand Saeid

Open Access

|Nov 2025

Abstract

In this study, Sheffer stroke Nelson algebras (briefly, s-Nelson algebras), (ultra) ideals, quasi-subalgebras, quotient sets, and fuzzy structures on these algebraic structures are introduced. The relationships between s-Nelson and Nelson algebras are analyzed. It is also shown that an s-Nelson algebra is a bounded distributive modular lattice, and the family of all ideals forms a complete distributive modular lattice. A congruence relation on an s-Nelson algebra is determined by an ideal and quotient s-Nelson algebras are constructed by this congruence relation. Finally, it is indicated that a quotient s-Nelson algebra constructed by the ultra ideal is totally ordered and that the cardinality of the quotient is less than or equal to 2.

References

J. C. Abbott, Implicational algebras, Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie 11(59) (1967), 3-23.
Search in Google Scholar Back to article
S. Burris and H. P. Sankappanavar, A course in universal algebra, Graduate Texts Math 78 (1981).
Search in Google Scholar Back to article
I. Chajda, Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 44(1) (2005), 19-23.
Search in Google Scholar Back to article
I. Chajda, R. Halaš and H. Länger, Operations and structures derived from non-associative MV-algebras, Soft Computing 23 (2019), 3935-3944.
Search in Google Scholar Back to article
I. Chajda and H. Länger, Sheffer operation in relational systems, Soft Computing 26 (2022), 89-97.
Search in Google Scholar Back to article
W. B. Ewald, Intuitionistic tense and modal logic, Journal of Symbolic Logic 51(1) (1986), 166-179.
Search in Google Scholar Back to article
A. V. Figallo and G. Pelaitay, An algebraic axiomatization of the Ewalds intuitionistic tense logic, Soft Computing 18 (2014), 1873-1883..
Search in Google Scholar Back to article
A. V. Figallo, G. Pelaitay and J. Sarmiento, An algebraic study of tense operators on Nelson algebras, Studia Logica 19 (2021), 285-312.
Search in Google Scholar Back to article
U. Rivieccio and M. Spinks, Quasi-Nelson; or, non-involutive Nelson algebras. In: D. Fazio, A. Ledda, F.Paoli (eds.), Algebraic Perspectives on Substructural Logics. Trends in Logic, Springer 55 (2020), 133-168.
Search in Google Scholar Back to article
U. Rivieccio and R. Jansana, Quasi-Nelson algebras and fragments, Mathematical Structures in Computer Science 31(3) (2021), 257-285.
Search in Google Scholar Back to article
C. Gomez, M. A. Marcos and H. J. San Martin, On the relation of negations in Nelson algebras, Reports on Mathematical Logic 56 (2022), 15-56.
Search in Google Scholar Back to article
T. Katican, T. Oner, A. Rezaei and F. Smarandache, Neutrosophic N-structures applied to Sheffer stroke BL-algebras, Computer Modeling in Engineering and Sciences 129(1) (2021), 355-372.
Search in Google Scholar Back to article
A. A. Markov, A constructive logic, Journal of Sysmbolic Logic 18(3) (1953), 257-257.
Search in Google Scholar Back to article
W. McCune, R. Vero, B. Fitelson, K. Harris, A. Feist and L. Wos, Short single axioms for Boolean algebra, Journal of Automated Reasoning 29 (2002), 1-16.
Search in Google Scholar Back to article
A. Molkhasi and K. P. Shum, Representations of strongly algebraically closed algebras, Algebra and Discrete Mathematics 28(1) (2019), 130-143.
Search in Google Scholar Back to article
A. Molkhasi, Representations of Sheffer stroke algebras and Visser algebras, Soft Computing 25 (2021), 85338538.
Search in Google Scholar Back to article
D. Nelson, Constructible falsity, Journal of Symbolic Logic 14(1) (1949), 16-26.
Search in Google Scholar Back to article
T. Oner, T. Katican, A. Borumand Saeid and M. Terziler, Filters of strong Sheffer stroke non-associative MV-algebras, Analele Stiintifice ale Universitatii Ovidius Constanta 29(1) (2021), 143-164.
Search in Google Scholar Back to article
T. Oner, T. Katican and A. Borumand Saeid, Fuzzy Filters of Sheffer stroke Hilbert algebras, Journal of Intelligent and Fuzzy Systems 40(1) (2021), 759-772.
Search in Google Scholar Back to article
T. Oner, T. Katican and A. Borumand Saeid, Relation between Sheffer stroke and Hilbert algebras, Categories and General Algebraic Structures with Applications 14(1) (2021), 245-268.
Search in Google Scholar Back to article
H. Rasiowa, N-lattices and constructive logic with strong negation, Fundamenta Mathematicae 46(1) (1958), 61-80.
Search in Google Scholar Back to article
H. Rasiowa, An algebraic aproach to non-classic logics, Warzawa & Amsterdam: North-Holland Publishing Company, (1974).
Search in Google Scholar Back to article
S. Burris and H. P. Sankappanavar, A course in universal algebra, Graduate Texts Math, 78 (1981).
Search in Google Scholar Back to article
H. M. Sheffer, A set of five independent postulates for Boolean algebras, with application to logical constants, Transactions of the American Mathematical Society 14(4) (1913), 481-488.
Search in Google Scholar Back to article
R. Vero, A shortest 2-basis for Boolean algebra in terms of the Sheffer stroke, Journal of Automated Reasoning 31 (2003), 1-9.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2025-0030 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 93 - 119

Submitted on: Apr 25, 2024

Accepted on: Oct 8, 2024

Published on: Nov 29, 2025

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Related subjects:

© 2025 Tahsin Oner, Tugce Katican, Arsham Borumand Saeid, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 33 (2025): Issue 3 (October 2025)