Description: Let $k$ be a countable field and $S=k[x_1, x_2, x_3,\ldots ]$ be the polynomial ring in countably many variables. Let $I$ be the ideal generated by $\{x_i^2\mid i\in \mathbb N\}\cup\{x_ix_j\mid i, j\in \mathbb N, j\geq 2i\}$. The ring is $R=S/I$.

Keywords polynomial ring quotient ring

Reference(s):

Known Properties

Legend

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

Name | Measure | |
---|---|---|

cardinality | $\aleph_0$ | |

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

Krull dimension (classical) | 0 |

Name | Description |
---|---|

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