Volume 18, Issue 2 (10-2023)
IJMSI 2023, 18(2): 25-30 |
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Dorbidi H R. Some Classes of Weakly Prime Center Rings. IJMSI 2023; 18 (2) :25-30
URL: http://ijmsi.ir/article-1-1066-en.html
URL: http://ijmsi.ir/article-1-1066-en.html
Abstract:
Let R be a ring. The ring R is called weakly prime center(WPC ring) if ab∈Z(R) implies that aRb is an ideal of R. In this paper, we prove that every left(right) duo ring is a WPC ring. Also we prove that some classes of rings with nilpotent Jacobson radical are WPC rings. Finally, we prove that a simple ring is a WPC ring if and only if it is a domain.
Type of Study: Research paper |
Subject:
General
References
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2. T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, 2001. [DOI:10.1007/978-1-4419-8616-0] [PMID]
3. L. H. Rowen, Ring Theory (Student edition), Academic Press. London-Newyork, 1991.
4. J. C. Wei, On Rings with Weakly Prime Centers, J. Ukrain. Math, 66(12), (2015), 1812-1822. [DOI:10.1007/s11253-015-1053-9]
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