Algebra and Logic Seminar

The next meeting of the seminar will be held on September 29, 2017 (Friday), at 12:45, in Room 578 of the Institute of Mathematics and Informatics.

A talk on

GENERALIZING NIL CLEAN RINGS

will be delivered by Peter DANCHEV.

Everybody is invited.

Abstract. We introduce the class of unipotently nil clean rings as those rings R in which for every a ∈ R there exist an idempotent e and a nilpotent q such that a − e − 1 − q ∈ (1 − e)Ra.

Each unipotently nil clean ring is weakly nil clean in terms of Ster (J. Algebra, 2014), and hence it is exchange, as well as each nil clean ring is unipotently nil clean. Our results obtained here considerably extend these of Diesl (J. Algebra, 2013) and Danchev-Ster (Taiwanese J. Math., 2015).

The obtained results will be published in Bull. Belgian Math. Soc. Simon Stevin 25 (2018).