Generalized Baеr and Generalized Quasi-Baеr Properties of Skеw Generalized Power Series Rings | ||||
| Assiut University Journal of Multidisciplinary Scientific Research | ||||
| Volume 54, Issue 1, January 2025, Page 170-180 PDF (706.9 K) | ||||
| Document Type: Novel Research Articles | ||||
| DOI: 10.21608/aunj.2024.333328.1099 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Refaat Mohamed Salem1; Ramy Abdel-Khalek2; Mostafa Hamam  3
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| 1Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt | ||||
| 2Department of Mathematics, Faculty of Science, Al Azhar University. | ||||
| 3Mathematics Department, Faculty of Science, Assiut university, Assiut, Egypt. | ||||
| Abstract | ||||
| Let R be a ring with identity, (S,≤) an ordered monoid, ω:S→End(R) a monoid homomorphism, and A=R[[S,ω]] the ring of skew generalized power series. The concepts of generalized Baer and generalized quasi-Baer rings are generalization of Baer and quasi-Baer rings, respectively. A ring R is called generalized right Baer (generalized right quasi-Baer) if for any non-empty subset S (right ideal I) of R, the right annihilator of 〖S 〗^n (I^n) is generated by an idempotent for some positive integer n. Left cases may be defined analogously. A ring R is called generalized Baer (generalized quasi-Baer) if it is both generalized right and left Baer (generalized right and left quasi-Baer) ring. In this paper, we examine the behavior of a skew generalized power series ring over a generalized right Baer (generalized right quasi-Baer) ring and prove that, under specific conditions, the ring A is generalized right Baer (generalized right quasi-Baer) if and only if R is a generalized right Baer (generalized right quasi-Baer) ring. | ||||
| Keywords | ||||
| generalized Baer rings; generalized quasi-Baer rings; generalized power series ring; skew generalized power series ring | ||||
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