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Oct 23, 2010 at 12:17 comment added Andreas Thom I see. This also implies that every unit in such a monoid ring contains 1 in its support. That is were I went wrong. I thought existence of non-trivial left-invertible elements would be a consequence of the existence of units in the monoid ring, but that is wrong. I hope you allow me to change the question slightly.
Oct 23, 2010 at 11:52 history answered Torsten Ekedahl CC BY-SA 2.5