Title: My bad!
Product review: Sorry, in reference to the ring controversy below, the original reviewer is correct. The authors state (correctly) that a non-empty subset is a subring iff closed under subtraction and multiplication. Then they say if the subset has identity, only addition and multiplication are required. This is _almost_ true...actually, if a subset has -1 (the additive inverse of the multiplicative identity of the larger ring), then addition and multiplication are enough. I didn't read closely enough. My apologies! In any case, in a book of this size, errors like this are bound to occur occasionally. I didn't find the number of errors in this book excessive or distracting.
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