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 rings.Abstract
Replacing left principal ideals by cosets in the monoid (R, ·) of a unital ring R, we say that an element a ∈ R is left unit exchange (or suitable) if there is an idempotent e ∈ R such that e − a ∈ 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.
Mathematics Subject Classification (2010): 16U99, 16U60, 13G99.
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