Weakly UU rings

Abstract

We introduce and give a comprehensive study of weakly UU rings, calling them WUU rings. This notion is a natural generalization of the so-called UU rings, defined by Calugareanu (Carpath. J. Math., 2015) and investigated in details by Danchev-Lam (Publicat. Math. Debrecen, 2016). It also demarcates the strength of recent results about these kind of rings by giving a strong barrier between some of their crucial properties.