A nonzero ring is called a UN-ring if every nonunit is a product of a unit and a nilpotent
element. We show that all simple Artinian rings are UN-rings and that the UN-rings whose …

A nonzero ring is said to be fine if every nonzero element in it is a sum of a unit and a
nilpotent element. We show that fine rings form a proper class of simple rings, and they …

A ring R is a UU ring if every unit is unipotent, or equivalently if every unit is a sum of a
nilpotent and an idempotent that commute. These rings have been investigated in …

Nil-Good Unital Rings 1 Introduction and Terminology Page 1 International Journal of
Algebra, Vol. 10, 2016, no. 5, 239 - 252 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.6212 …

We study the class of almost uniserial rings as a straightforward common generalization of
left uniserial rings and left principal ideal domains. A ring R is called almost left uniserial if …

Rings in which elements are sums of nilpotents, idempotents and tripotents Page 1 Journal of
Algebra and Its Applications Vol. 17, No. 1 (2018) 1850009 (7 pages) c© World Scientific …

Let R be a ring and let N denote the set of nilpotent elements of R. Let n be a nonnegative
integer. The ring R is called a θ n-ring if the number of elements in R which are not in N is at …

In this article we introduce the notion of nil elements and even square rings and provide
some examples. Nil elements are special type of nilpotent elements and possess interesting …

Let $ R $ be a 2-primal strongly 2-nil-clean ring. We prove that every square matrix over $ R
$ is the sum of a tripotent and a nilpotent matrices. The similar result for rings of bounded …

In this paper, we study rings that are additively generated by units. We prove that if the
identity in a ring with stable range one is a sum of two units, then every (von Neumann) …