if I define The plane: ##F = ℝ## x ##ℝ = \{ (a, b) | a, b ∈ ℝ \} ##(adsbygoogle = window.adsbygoogle || []).push({});

and define addition and multiplication as:

(a, b) + (c, d) := (a + c, b + d)

(a, b) · (c, d) := (ac, bd)

Then ##F## is a field. right?

would the multiplication as described here make ℂ a field?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Field if I define The plane

Loading...

Similar Threads - Field define plane | Date |
---|---|

I Need clarification on a theorem about field extensions/isomorphisms | Dec 19, 2017 |

I Splitting Fields: Anderson and Feil, Theorem 45.6 ... | Jun 23, 2017 |

I Splitting Fields: Anderson and Feil, Theorem 45.5 ... | Jun 22, 2017 |

I Splitting Fields: Anderson and Feil, Theorem 45.4 ... | Jun 21, 2017 |

I How this defines a linear transformation | Apr 25, 2016 |

**Physics Forums - The Fusion of Science and Community**