Semi-Baer and Semi-Quasi Baer Properties of Skew Generalized Power Series Rings | ||
| Assiut University Journal of Multidisciplinary Scientific Research | ||
| Volume 53, Issue 2, May 2024, Pages 255-266 PDF (593.76 K) | ||
| Document Type: Novel Research Articles | ||
| DOI: 10.21608/aunj.2024.256321.1072 | ||
| Authors | ||
| Mostafa Hamam* 1; Ramy El-Sayed Abdel-Khaleq2; Refaat Mohamed Salem2 | ||
| 1Mathematics Department, Faculty of Science, Assiut university, Assiut, Egypt. | ||
| 2Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, 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 semi-Baer and semi-quasi Baer rings were introduced by Waphare and Khairnar as extensions of Baer and quasi-Baer rings, respectively. A ring R is called a semi-Baer (semi-quasi Baer) ring if the right annihilator of every subset (right ideal) of R is generated by a multiplicatively finite element in R. In this paper, we examine the behavior of a skew generalized power series ring over a semi-Baer (semi-quasi Baer) ring and prove that, under specific conditions, the ring A is semi-Baer (semi-quasi Baer) if and only if R is semi-Baer (semi-quasi Baer). Also, we prove that if f is a multiplicative finite element of A, then f (1) is a multiplicative finite element of R and determine the conditions under which f = c_(f(1)). | ||
| Keywords | ||
| Baer rings; quasi-Baer rings; semi-Baer rings; semi-quasi Baer rings; generalized power series ring | ||
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