N. K. Godara

Characterization of Integrally Closed Simple Extensions of Valuation Rings

Let $$v$$ be a Krull valuation on a field, with valuation ring $$R_v$$ . Consider the irreducible polynomial $$F(x) = x^n + a(bx^k + c)^m$$ in $$R_v[x]$$ , where $$1 \leq km < n$$ , and let $$\theta$$ be a root of $$F(x)$$ . This paper establishes necessary and sufficient conditi...