Commutative ring detail


Name: Clark's uniserial ring

Description: Let $D=F[[x]]$ and let $Q$ be the field of fractions of $D$. Set $V=Q/D$. The ring is the trivial extension $(D, V)$

Notes: Krull dimension 2

Keywords trivial extension power series ring

Reference(s):

  • Nicholson, W. Keith; Mohamed F. Yousif., Quasi-Frobenius Rings., Vol. 158. Cambridge University Press, (2003). P 133-134 Ex 6.6