Some Properties of Unit, Zero-Divisor and Idempotent Elements of the Ring of Dual Numbers of the Ring Zn, Zn[α]
DOI:
https://doi.org/10.59992/IJSR.2025.v4n9p10الكلمات المفتاحية:
Ring of Integers modulo n، Ring of Dual Numbers، Unit Element، Zero-Divisor Elementالملخص
For any commutative ring with unity R, a new ring can be defined called the ring of dual numbers of the ring R, denoted by R[α]. In this paper we obtain a characterization of unit and zero-divisor elements in the ring of dual numbers of the ring of integers modulo n, Zn[α].
المراجع
1. D. D. Anderson and Sangmin Chun, Irreducible Elements in Rings with Zero Divisors, Housten Journal of Mathematics, 37, (2011) 741- 744.
2. D. D. Anderson and Silvia Voldes-Leon, Factorization in Commutative Rings with Zero Divisors, Rocky Mountain Journal of Mathmatics 26 (1996) 439-479.
3. Adam A. Allan, Micheal J. Dunne, John R. Jack, Justin C. Lynd and Harold W.Ellingsen Jr, Classification of the group of units in Gaussian integers modulo n,Mu Epsilon Journal 12 (9) (Fall 2008), 513-519.
4. S. Galovich, Unique Factorization Rings With Zero Divisors, Math Magazine 51(1978) 276-283.
5. Suman Mondal and Dhiren K Basnet, Idempotent of Zn, arxiv 2410.14576v1.
6. Thomas Q Sibley. Idempotents `a la mod. The College Mathematics Journal, 43(5):401–404, 2012.
7. Gaurav Mittal. Non trivial idempotents of the matrix rings over poly- nomial ring Zpqr[x].preprint.
