2025/10/26 by Danchev, Peter, Doostalizadeh, Mina, Esfandiar, Mehrdad +1
#16S34 #16U60 #20C07 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2510.22611
We investigate the so-called \it UJ# rings, a new type of rings in which every unit can be written as 1+j with j∈ J#(R). These rings were defined and studied by Saini-Udar in Czechoslovak Math. J. (2025) under the name \it √(J)U rings. (See \citeSU.) This class extends both the classes of UU and UJ rings, but also has its own special properties. In this study, we present some additional results about UJ# rings that supply those from \citeSU explaining their connections with Dedekind-finite, semi-potent and Boolean rings, respectively, as well as we give several characterizations in this direction. We also examine how these rings behave under common ring constructions and find conditions for group rings to be UJ#. Moreover, our establishments shed a clearer picture of how unit elements interact with radical-like parts of a ring.