A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

We introduce the notion of weakly quasi invo-clean rings where every element $ r can be written as r=v+e or r=v-e $, $v\in Qinv(R)$ and e\in Id(R) $. study various properties elements rings. prove that ring R=\prod_{i\in I} R_i all are invo-clean, is if only factors but one invo-clean.