2014/12/14 by Peter Danchev, Danchev, Peter, Janez Šter +1
Mathematics · #16E50 #16S70 #16U70 #16U99 #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1412.4359
openalex publication_date 2014/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the class weakly nil clean rings, as rings R in which for every a∈ R there exist an idempotent e and a nilpotent q such that a-e-q∈ eRa. Every weakly nil clean ring is exchange. Weakly nil clean rings contain pi-regular rings as a proper subclass, and these two classes coincide in the case of central idempotents. Every weakly nil clean ring of bounded index and every weakly nil clean PI-ring is strongly pi-regular. The center of a weakly nil clean ring is strongly pi-regular, and consequently, every weakly nil clean ring is a corner of a clean ring. These results extend Azumaya [3], McCoy [24], and the second author [33] to a wider class of rings and provide partial answers to some open questions in [13] and [33]. Some other properties are also studied and several examples are given.