Rings such that, for each unit u, u − u n belongs to the Jacobson radical

Abstract

A ring R is said to be n-UJ if u − u n ∈ J(R) for each unit u of R, where n > 1 is a fixed integer. In this paper, the structure of n-UJ rings is studied under various conditions. Moreover, the n-UJ property is studied under some algebraic constructions. Mathematics Subject Classification (2010). 16N20, 16D60, 16U60, 16W10

Keywords

• UU-ring
• UJ-ring
• unit
• Jacobson radical
• clean ring
• (semi)regular ring
• reduced ring

References

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