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On Irreducible Divisor Graphs in Commutative Rings with Zero-Divisors
並列摘要
In this paper, we continue the program initiated by I. Beck's now classical paper concerning zero-divisor graphs of commutative rings. After the success of much research regarding zero-divisor graphs, many authors have turned their attention to studying divisor graphs of non-zero elements in integral domains. This inspired the so called irreducible divisor graph of an integral domain studied by J. Coykendall and J. Maney. Factorization in rings with zero-divisors is considerably more complicated than integral domains and has been widely studied recently. We find that many of the same techniques can be extended to rings with zero-divisors. In this article, we construct several distinct irreducible divisor graphs of a commutative ring with zero-divisors. This allows us to use graph theoretic properties to help characterize finite factorization properties of commutative rings, and conversely.
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延伸閱讀
- Boua, A., Raji, A., Ali, A., & Ali, F. (2015). On Generalized Semiderivations of Prime Near Rings. International Journal of Mathematics and Mathematical Sciences, 2015(), 250-256. https://doi.org/10.1155/2015/867923
- Yang, C. C. (2009). Finiteness properties of higher generalized derivations in prime rings. [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2009.10626
- Chaudhry, M. A., Golbasi, O., & Koc, E. (2015). Some Results on Generalized (α, β)-Derivations in *-Prime Rings. International Journal of Mathematics and Mathematical Sciences, 2015(), 194-199. https://doi.org/10.1155/2015/583050
- Dhara, B., & Pattanayak, A. (2012). On Generalized (σ, τ)-Derivations in Semiprime Rings. ISRN Algebra, (in press), 3-9. https://doi.org/10.5402/2012/120251
- Dhara, B., & Sharma, R. K. (2010). On the Annihilators of Derivations with Engel Conditions in Prime Rings. Tamsui Oxford Journal of Mathematical Sciences, 26(3), 255-264. https://doi.org/10.6988/TOJMS.201008.0255