TITLE: Definition of Ring Vs Rng
QUESTION [13 upvotes]: When I took abstract algebra I learned that a ring was a set that is an abelian group under addition and monoid under multiplication (along with the distributive property). 
In preperation to tutor someone in algebra I've noticed that some books present a ring as what I know as a "rng" or an abelian group under addition and a semi-group under multiplication.
Is there any reason to prefer one as the definition for a ring vs the other?
EDIT
And a very related question, is there any math authority or consensus that has dictated/specified that it is more correct to use the ring/ring with unity or the rng/ring definition?

REPLY [6 votes]: Wikipedia had a large discussion of this from 2003 to 2008 including an analysis of publications, and comments about both Bourbaki and Cambridge University changing to require a 1. 
There does not seem to be a consensus, but there does seem to be a trend towards more modern and more advanced texts being more likely to require a 1.