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math.GR2025
Adjoining universal inverses to families of elements of free monoids
George M. Bergman
Let be the free monoid on a generating set , and suppose one adjoins to universal 2-sided inverses to a finite set of its elements. We note an elementary algorit…
math.RA2025
Strongly clean ring elements that are one-sided inverses
George M. Bergman
A longstanding open question is whether every strongly clean ring (ring in which every element is strongly clean, i.e., is the sum of an idempotent and a unit which commute with ea…