Algebraic properties of rings of generalized power series

✍ Scribed by Daniel Pitteloud

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 242 KB
• Volume: 116
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(01)00099-9

✦ Synopsis

The ÿelds K((G)) of generalized power series with coe cients in a ÿeld K and exponents in an additive abelian ordered group G play an important role in the study of real closed ÿelds. The subrings K((G 60 )) consisting of series with non-positive exponents ÿnd applications in the study of models of weak axioms for arithmetic. Berarducci showed that the ideal J ⊆ K((G 60 )) generated by the monomials with negative exponents is prime when G = (R; +) is the additive group of the reals, and asked whether the same holds for any G. We prove that this is the case and that in the quotient ring K((G 60 ))=J , each element (not in K) admits at least one factorization into irreducibles.