Galoitica: Journal of Mathematical Structures and Applications
Journal DOI
2834-5568ISSN (Online)
Volume 10 , Issue 1 , PP: 39-55, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Sundus taha kathem 1 * , Abdulrahman Hameed Majeed 2
Doi: https://doi.org/10.54216/GJMSA.0100105
The concept of inverse Γ-semiring M is a generalization of inverse semiring. This paper investigates the concept (σ, τ)- derivation on inverse Γ-semiring and extend a few results of this map on prime inverse Γ- semiring that acts as a homomorphism or as an anti- homomorphism, where σ, τ are automorphisms on M.
, (&sigma , , &tau , )- derivation , Inverse &Gamma , -semiring , Jordan ideal , Left ideal , Prime inverse &Gamma , -semiring
[1] Argaç, N., Kaya, A., & Kisir, A. (1987). (σ, τ)-derivations in prime rings. Mathematical Journal of Okayama University, 29(1), 173–177.
[2] Ashraf, M., Rehman, N. and Quadri.(1999). M. A. On (σ, τ)-derivations in certain classes of rings, Rad. Mat. 9, 187–192.
[3] Barnes, W. (1966). On the Γ-rings of Nobusawa. Pacific Journal of Mathematics, 18(3), 411–422.
[4] Bell, H. E. and Kappe, L. C.(1989). Rings in which derivations satisfy certain algebraic conditions, Acta. Math. Hungar. 53, 339–346.
[5] Cranford, S. W. (2020). Seven Seconds or Less: Buzzwordy Titles in the Era of MOFs and Tinder. Matter, 3(4), 965–967.
[6] Cronje, J. C. (2020). Designing Questions for Research Design and Design Research in e‑Learning. Electronic Journal of E-Learning, 18(1), pp13-24.
[7] Fakieh, W. M., & Alhawiti, F. A. (2021). Ideal Theory in Commutative Γ-Semirings. International Journal of Algebra, 15(2), 77–101.
[8] Fryer, L. K., & Dinsmore, D. L. (2020). The Promise and Pitfalls of Self-report: Development, research design and analysis issues, and multiple methods. Frontline Learning Research, 8(3), 1–9.
[9] Grieshaber, S. (2020). Equity and research design. In Doing early childhood research (pp. 177–191). Routledge.
[10] Halder, A. K. (2022). Commutativity of Prime Γ-MA-semirings with None-zero Jordan Left Derivations and Left Derivations on Closed Lie Ideals. International Journal of Research in Engineering and Science, 10(12), 439–444.
[11] Hamil, S. A. (2021). Commutativity of Prime Γ-Semirings with Derivations and Generalized Derivations. Journal of Physics: Conference Series, 1804(1), 12091.
[12] Ibraheem, R. K. H., & Majeed, A. H. (2019). On Lie Structure in Semiprime Inverse Semirings. Iraqi Journal of Science, 2711–2718.
[13] Mandal, D. (2014). Neutrosophic Ideals of¡-Semirings. Journal of New Results in Science, 3(6), 51–61.
[14] Nobusawa, N. (1964). On a generalization of the ring theory.
[15] Paul, A. C., & Chakraborty, S. (2015). Derivations acting as homomorphisms and as antihomomorphisms in σ-lie ideals of σ-prime gamma rings. Mathematics and Statistics, 3(1), 10–15.
[16] Rao, M. M. K. (1995). Γ-semirings-I. Southeast Asian Bull. Math, 19(1), 49–54.
[17] Rao, M. M. K. (1997). G-Semirings--II. Southeast Asian Bulletin of Mathematics, 21(3), 281–288.
[18] Rasheed, M. K., Hameed, F. A., & Majeed, A. H. (2020). On Generalized (α, β) Derivation on Prime Semirings. Journal of Physics: Conference Series, 1591(1), 12080.
[19] Rasheed, M. K., & Majeed, A. H. (2019). Some Results of (α, β) Derivations on Prime Semirings. Iraqi Journal of Science, 60(5), 1154–1160.
[20] Salih, S. M., & Karim, M. O. (2015). Centralizing (Sigma, Tau)-Derivations on Prime Gamma-Rings. Mathematical Theory and Modeling, 5(4).
[21] Saragih, M., & Novimariono, N. (2020). An Experimental Study of The Effectiveness PEOW MODEL Through Applying Quartet Card in Teaching English Writing. Indonesian Journal of Education, Social Sciences and Research (IJESSR), 1(1), 32–40.
[22] Shu, K., Mahudeswaran, D., Wang, S., Lee, D., & Liu, H. (2020). Fakenewsnet: A data repository withnews content, social context, and spatiotemporal information for studying fake news on social media. Big Data, 8(3), 171–188.
[23] Stewart, E. (2021). Detecting Fake News: Two Problems for Content Moderation. Philosophy & Technology, 1–18.
[24] van der Giesen, C., Cucurachi, S., Guinée, J., Kramer, G. J., & Tukker, A. (2020). A critical view on the current application of LCA for new technologies and recommendations for improved practice. Journal of Cleaner Production, 259, 120904.
[25] Zaghir, K. A. D., & Majeed, A. H. (2021). (α, β)–Derivations on Prime Inverse Semirings. Iraqi Journal of Science, 4081–4091.
