SOME PROPERTIES OF CLEAR RINGS
DOI:
https://doi.org/10.25077/jmua.15.2.196-212.2026Keywords:
clean ring, clear ring, unit regular, unitAbstract
Let (R, +, ·) be a ring with unity. An element in R is called a clean
element if it is the sum of a unit element and an idempotent element. A ring R is called
a clean ring if all elements in R are clean elements. The notion of a clean element was
generalized to a clear element by replacing the idempotent element with a unit-regular
element. An element in R is called a clear element if it is the sum of a unit element
and a unit-regular element. A ring R is called a clear ring if all elements in R are clear
elements. In this paper, we study the new properties of clear elements in a ring and
clear properties in certain special rings, such as opposite rings, quotient rings, corner
rings, Morita rings, and group rings.
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