The ring of Hahn series with value group? , denoted , is the ring of functions such that is well-ordered when considered as a subset of the opposite poset . Addition is defined pointwise, and multiplication is defined by the convolution product:
As a corollary, if is divisible, is real closed if is real closed. This is because the adjunction of a square root of would make algebraically closed, since this gives the same result as constructing the Hahn series over the algebraically closed field .
Revised on February 5, 2012 03:27:18
by Todd Trimble