2020/01/09 by Debraj Roy, Roy, Debraj, Tikaram Subedi +1
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.2001.02864
arxiv created 2020/01/09 · arxiv updated 2020/01/10
In this paper, we introduce and study a strict generalization of symmetric rings. We call a ring R 'P-symmetric' if for any a, b, c∈ R, abc=0 implies bac∈ P(R), where P(R) is the prime radical of R. It is shown that the class of P-symmetric rings lies between the class of central symmetric rings and generalized weakly symmetric rings. Relations are provided between P-symmetric rings and some other known classes of rings. From an arbitrary P-symmetric ring, we produce many families of P-symmetric rings.