# RINGS CLOSE TO SEMIREGULAR

• Aydogdu, Pinar ;
• Lee, Yang ;
• Ozcan, A. Cigdem
• Published : 2012.05.01
• 50 11

#### Abstract

A ring $R$ is called semiregular if $R/J$ is regular and idem-potents lift modulo $J$, where $J$ denotes the Jacobson radical of $R$. We give some characterizations of rings $R$ such that idempotents lift modulo $J$, and $R/J$ satisfies one of the following conditions: (one-sided) unit-regular, strongly regular, (unit, strongly, weakly) ${\pi}$-regular.

#### Keywords

idempotent lifting;semi unit-regular ring;semi (strongly) ${\pi}$-regular ring

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#### Acknowledgement

Supported by : National Research Foundation of Korea(NRF)