  This article introduces the notion of an NJ-reflexive ring and demonstrates
that it is distinct from the concept of a reflexive ring. The class of
NJ-reflexive rings contains the class of semicommutative rings, the class of
left (right) quasi-duo rings, and the class of J-clean rings but is strictly
larger than these classes. Additionally, the article investigates a sufficient
condition for NJ-reflexive rings to be left (right) quasi-duo, as well as some
conditions for NJ-reflexive rings to be reduced. It also explores extensions of
NJ-reflexive rings and notes that the NJ-reflexive property may not carry over
to polynomial extensions.
