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In analogy to the elementwise definitions of UU- and UJ-rings, a ring Formula: see text is called UNJ if Formula: see text. After presenting several characterizations and properties, we consider the UNJ-rings within many well-studied classes of rings. In particular, we examine Dedekind finite rings, 2-primal rings, (semi)regular rings, Formula: see text-regular rings and rings that satisfy the identity Formula: see text. Finally, we conclude this paper with group UNJ-rings.
Koşan et al. (Wed,) studied this question.
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