# center (rings)

If $A$ is a ring, the center of $A$, sometimes denoted $\mathrm{Z}(A)$, is the set of all elements in $A$ that commute with all other elements of $A$. That is,

$$\mathrm{Z}(A)=\{a\in A\mid ax=xa\forall x\in A\}$$ |

Note that $0\in \mathrm{Z}(A)$ so the center is non-empty. If we assume that $A$ is a ring with a multiplicative unity $1$, then $1$ is in the center as well. The center of $A$ is also a subring of $A$.

Title | center (rings) |
---|---|

Canonical name | Centerrings |

Date of creation | 2013-03-22 12:45:29 |

Last modified on | 2013-03-22 12:45:29 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 6 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 16U70 |

Synonym | center |

Related topic | GroupCentre |