Let $D=k[[x]]$ for a countably infinite field $k$ and let $Q$ be the field of fractions of $D$. Set $V=Q/D$. The ring is the trivial extension $T(D, V)$

Keywords power series ring trivial extension

- W. K. Nicholson and M. F. Yousif. Quasi-Frobenius Rings. (2003) @ Ex 6.6 , pp 133-134

Known Properties

Legend

- = has the property
- = does not have the property
- = information not in database

Name | Measure | |
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cardinality | $\mathfrak c$ | |

composition length | left: $\infty$ | right: $\infty$ |

Krull dimension (classical) | 1 |

Name | Description |
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Idempotents | $\{0,1\}$ |