do you need a Noether ring for Noetherian Theorem? just wondering if a Noetherian ring has any relation to the conservation law of Noether's Theorem?  I thought I read the universal enveloping algebra can fall under a Noetherian ring, and was wondering if a Noetherian ring implies Noether's Theorem?
 A: They are just both eponymously named after the same person, Emmy Noether.
Noether's theorem is couched mostly in terms of mathematical physics, and is a statement about symmetries on a space evolving according to some Lagrangian. While a Noetherian ring might be found while doing Lagrangian mechanics, they are not vital to the statement of Noether's theorem.
There is a nifty little book by Neuenschwander called Emmy Noether's Wonderful Theorem which I found to be very accessable.
By the way, when seeing other things named "Noether," you might want to be on your guard: Emmy's father was a productive mathematician as well as her :) See this, for example.
There is a footnote in T.Y. Lam's Lectures on Modules and rings about the Lasker-Noether theorem on primary decomposition of modules (p 102):

The Lasker-Noether Theorem was originally named after the chess master and mathematician Emanuel Lasker and Emmy's father, Max Noether. The version of this theorem for a commutative Noetherian ring should perhaps be more appropriately called the "Lasker-Noether-Noether Theorem". Incidentally, Noether herself never knew that the rings satisfying her Endlichkeitsbedingung ["finiteness condition," referring to the ascending chain condition] were to be christened Noetherian rings. This term was coined by Claude Chevalley only in 1943; Emmy died in 1935...

