Unit exchange elements in rings
DOI:
https://doi.org/10.24193/subbmath.2020.3.02Keywords:
clean element, unit- regular element, exchange (suitable) element, unit suitable element, matrix ringsAbstract
Replacing left principal ideals by cosets in the monoid (R, ·) of a unitalring R, we say that an element a 2 R is left unit exchange (or suitable)
if there is an idempotent e 2 R such that e − a 2 U(R)(a − a2) where
U(R) denotes the set of units. Unit-regular and clean elements are left
(and right) unit suitable, and left (or right) unit suitable elements are
exchange (suitable).
The paper studies the multiple facets of this new notion.
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