It is well known that the monoid ring of the free product of a free group and a free monoid over a skew field is a fir. We give a proof of this fact that is more direct than the proof in the literature.
@article{urn:eudml:doc:41126, title = {Monoid rings that are firs.}, journal = {Publicacions Matem\`atiques}, volume = {34}, year = {1990}, pages = {217-221}, zbl = {0706.16019}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41126} }
Pitarch, Andreu. Monoid rings that are firs.. Publicacions Matemàtiques, Tome 34 (1990) pp. 217-221. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41126/