2025/03/05 by Danchev, Peter, Javan, Arash, Hasanzadeh, Omid +1
#16 S34 #16 U60 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2503.03643
We define and consider in-depth the so-called CΔ rings as those rings R whose elements are a sum of an element in C(R) and of an element in Δ(R). Our achieved results somewhat strengthen these recently obtained by Ma-Wang-Leroy in Czechoslovak Math. J. (2024) as well as these due to Kurtulmaz-Halicioglu-Harmanci-Chen in Bull. Belg. Math. Soc. Simon Stevin (2019). Specifically, we succeeded to establish that exchange CΔ rings are always clean as well as that exchange CN rings are strongly clean. Likewise, we prove that, for any ring R, the ring of formal power series R[[x]] over R is CΔ if, and only if, so is R. And, furthermore, we show that, for any ring R, if the polynomial ring R[x] is a CΔ ring, then R satisfies the Köthe conjecture. Some other closely related things concerning certain extensions of CΔ rings are also presented.