Integral domain   I replaced a zerodivisor free commutative ring with more than one element with an integral domain JamesBWatson reverted the change saying No if you read further down it explicitly states taht there need not be a  Ring is often taken as implying a  but not always  However Wikipedia practice does currently define ring to have a multiplicative identity via monoid so using this longer phrase doesnt make the more general applicability any clearer    I think the best fix would be to start out discussing integral domains and then discuss the more general case of a pseudoring later in the article especially since AFAICT the field of fractions of a pseudoring which is not a ring doesnt necessarily contain the pseudoring contrary to the assertion that it is the smallest field in which it can be embedded  Thoughts