We prove that generating relations between the elements [r] = r²-r of a commutative ring are the following: [r+s] = [r]+[s]+rs[2] and [rs] = r²[s]+s[r].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-4-3, author = {Andrzej Pr\'oszy\'nski}, title = {Relations between Elements r$^2$-r}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {55}, year = {2007}, pages = {317-323}, zbl = {1129.13011}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-4-3} }
Andrzej Prószyński. Relations between Elements r²-r. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 317-323. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-4-3/