Chapter 8 - U.I.U.C. Math
... Noetherian, then the ring R[[X]] of formal power series is Noetherian. We cannot simply reproduce the proof because an infinite series has no term of highest degree, but we can look at the lowest degree term. If f = ar X r + ar+1 X r+1 + · · · , where r is a nonnegative integer and ar = 0, let us sa ...
... Noetherian, then the ring R[[X]] of formal power series is Noetherian. We cannot simply reproduce the proof because an infinite series has no term of highest degree, but we can look at the lowest degree term. If f = ar X r + ar+1 X r+1 + · · · , where r is a nonnegative integer and ar = 0, let us sa ...
Abstract Algebra
... from that to which you are accustomed; so a list of definitions of the terms we use is provided here. • The notation ‘f : A → B’ (read ‘f , from A to B’) means that f is a function with domain A and codomain B. In other words, f is a rule which assigns to every element a of the set A an element in t ...
... from that to which you are accustomed; so a list of definitions of the terms we use is provided here. • The notation ‘f : A → B’ (read ‘f , from A to B’) means that f is a function with domain A and codomain B. In other words, f is a rule which assigns to every element a of the set A an element in t ...
![[hal-00137158, v1] Well known theorems on triangular systems and](http://s1.studyres.com/store/data/015177460_1-823a690e284005713c70fc9e95ccaaf8-300x300.png)
