On uniquely clean elements

Abstract

We introduce a subclass of semipotent rings in which every element which is both uniquely clean and strongly clean can be written as a sum of a central idempotent and an element in the jacobson radical. This, in particular, settles a question left open in [4].

KEYWORD:

• Jacobson radical
• semipotent ring
• strongly clean ring
• uniquely clean element
• uniquely strongly clean element

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16N20
• 16U99