# support (graded ring)

Let $S$ be a groupoid (semigroup, group) and suppose $R={\oplus}_{s\in S}{R}_{s}$ is an $S$- graded ring^{}.

We define the support^{} of $r$ to be the set $\mathrm{supp}(r)=\{s\in S\mid {r}_{s}\ne 0\}$. We can extend this definition to $\mathrm{supp}(R)=\bigcup \mathrm{supp}{R}_{s}\ne 0\}$. If $\mathrm{supp}(R)$ is a finite set^{} then we say that the ring $R$ has finite
support.

Title | support (graded ring) |
---|---|

Canonical name | SupportgradedRing |

Date of creation | 2013-03-22 15:40:00 |

Last modified on | 2013-03-22 15:40:00 |

Owner | aplant (12431) |

Last modified by | aplant (12431) |

Numerical id | 6 |

Author | aplant (12431) |

Entry type | Definition |

Classification | msc 13A02 |

Related topic | GradedRing |

Defines | support |

Defines | finite support |