Abstract
Given a surjective ring homomorphism, we study when the induced group homomorphism on unit groups is surjective. To this end, we introduce notions of generalized inverses and units, as well as a class of rings such that the set of closed points in the spectrum is a closed set. It is shown that any surjection out of such a ring induces a surjection on unit groups.
Citation
Justin Chen. "Surjections of unit groups and semi-inverses." J. Commut. Algebra 13 (3) 323 - 331, Fall 2021. https://doi.org/10.1216/jca.2021.13.323
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