i understand that if two rings are isomorphic, and one ring is an integral domain, so must the other be.
however, consider two rings, both commutative rings with unity.  is it possible that one ring contains zero divisors and one does not while there exists an ring homomorphism between the two?
there could not be a isomorphism between the two rings because there would be no one to one or onto mapping between the two rings. but could there be an operation preserving mapping between an integral domain and a commutative ring with unity and with zero divisors? 
clearly if such a mapping did exists it would not seem to be one to one or onto, but does this rule out the potential of a homomorphism existing between the two?


Question: Should performance tests be instrumented by build tools?
Answer: Ask yourself: what kind of performance tests do you have, and how often do you need them to be run?


Tests for the "daily use"? Then make them part of your unit tests.
Just in the QA cycle of every release/deployment? Keep them as part of your integration tests (assumed those tests are run for every release/deployment).
Tests for an isolated part of your application, just needed once for optimizing purposes and then never again? Then keep them out of your CI cycle.


Running time of those tests will probably be a factor. If your performance tests need less than 20 minutes, you won't have much trouble to integrate them into your "nightly builds" on your CI server. If they need a week for a complete run, you obviously need a different strategy. 

And to my understanding, using an agile model like "Scrum" means to adapt your process to the software you are building, not vice versa. So no decision of "where to place your performance tests" may be final. If you have tests at the beginning which are very fast, and become slower the more you expand them over time, you may have to relocate them in your process, split them up, change them to your needs etc.