Volume 27 • Issue 1 • PP: 10-18 • 2026
Neutrosophic of γ-BCK -Algebra
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The most important applications of an algebra like BCK-Algebra. As a generalization of ring, we study γ- semi-ring and γ-ring in invarianent neutrosophic set. Neutrosophic concepts are widely used in the field of mathematics and other sciences, especially in studying the Algebra. In this paper, we present the concept of neutrosophic γ-BCK-Algebras as an example of this generalization. We also present neutrosophic sub-algebra, neutrosophic ideal and some other type structure algebraic. We proved that if f : AI → N I is a homomorphism of neutrosophic γ-BCK-algebras AI and NI, then f is injective if and only if neutrosophic ker(f ) = {0I}. Also, we presented, if NI be a normal neutrosophic subalgebra of neutrosophic γ-BCK- algebra AI, then ” ∼ N I ” is a congruence relation.
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References
[1] Zadeh, L. A. Fuzzy sets. Information Control, 8(3): 1965, 338-353.
[2] Smarandache, F. A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Lgics, American Research Press, Reoboth, NM, USA, 1998.
[3] C¸ etkin, V. Banu Pazar Varolz and Halis Ayg¨un. On neutrosophic submodules of a module. 46 (5), 2017, 791 799.
[4] A. Al-Quran, F. Al-Sharqi and A. M. Djaouti. q-Rung simplified neutrosophic set: A generalization of intuitionistic, Pythagorean and Fermatean neutrosophic sets. AIMS Mathematics, 10(4): 8615-8646, 2025.
[5] Chen, L.; and Wang, J. Applications of Neutrosophic Logic in Decision-Making Processes. Journal of Applied Mathematics and Computation. 200, 2024, 150-162.
[6] Olgun, N. and Khatib, A. Neutrosophic Modules. Journal of Biostatistics and Biometric Applications.3, 2018, 2.
[7] A. Hazaymeh and A. Bataihah, Neutrosophic fuzzy metric spaces and fixed points for contractions of nonlinear type. Neutrosophic Sets Systems, 77(1): 96-112, 2025.
[8] Agboola, A. A. A. On refined neutrosophic algebraic structures. Neutrosophic Sets and Systems, 10, 2015, 99-101.
[9] Abed, M. M. On Indeterminacy (Neutrosophic) of Hollow Modules, Iraqi Journal of Science, 63(6), 2022, 2650-2655.
[10] Olgan, N. and Khatib, A. ”Neutrosophic Modules,” Journal of Biometric Applications. 3(2), 2018
[11] Agboola, A.A.A.; Akinola, A.D. and Oyebola, O.Y. Neutrosophic Rings I. International J. Math. Combin. 4 2011, 1-14.
[12] Saleh, A.M. O On pseudo valuation module and injectivity property, Journal of Discrete Mathematical Sciences and Cryptography, 25(8), 2022, 2753-2757.
[13] Iseki, K.; S. Tanaka, An introduction to theory of BCK-algebras, Math. Japon. 23 1978, 1-26.
[14] M. U. Romdhini et al. Modeling uncertainties associated with decision-making algorithms based on similarity measures of possibility belief interval-valued fuzzy hypersoft setting. Neutrosophic Sets and Systems, 77: 282-309, 2025.
[15] Kandasamy, W. V.; & Smarandache, F. Basic neutrosophic algebraic structures and their application to fuzzy and neutrosophic models (Vol. 4). Infinite Study, (2004).
[16] Y. Al-Qudah, A. Jaradat, S. K. Sharma, and V. K. Bhat. Mathematical analysis of the structure of one- heptagonal carbon nanocone in terms of its basis and dimension. Physica Scripta, 99(5), 055252, 2024.
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