On Wnil-Injectivity

Let N(R) denote the set of nilpotent elements of a ring R. A ring R is said to be nil π-regular if for any a∈N(R) there exists n∈N and x∈R such that an aⁿ≠0 and aⁿ= aⁿxaⁿ. In this paper we introduce nil π-regular rings as a proper generalization of nil regular rings (n-regular rings) and study their relations with wnil-injective rings.