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11:17 AM
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Q: Are $D_r$ - rings substantially different from $Q_r$ - rings, if so, what example differentiates them?

blabla An element $x$ of an algebraic ring $S$ is said to be right quasiregular if there exists another element $y\in S$ such that $x\circ y=x+y+xy=0$. DEFINITION- A topological ring is said to be a $D_r$ - ring if its right quasiregular (r.q.r.) elements form a d-open set (union of open $F_{\s...

I will mention that on MO it is recommended to use at least one of the top-level tags. I am not exactly sure which ones to use here. (Some of the candidates might be (ra.rings-and-algebras), (ac.commutative-algebra) or (gn.general-topology). — Martin Sleziak 1 min ago
 
 
6 hours later…
5:24 PM
The OP added a top-level tag. After this, the post was also caught by the feeds in the bounty chatroom.
 

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