Let V be a countable dimensional vectorspace over a field F .(adsbygoogle = window.adsbygoogle || []).push({});

Let R denote End_F V .

Prove that V is a simple R-module. If $ e1 , e2 , . . .$ is a basis

of V , then we have a module homomorphism φ_j from R to V ,

sending f in R to f (e_j ).

Find the ker(φ_j) .

Find Jac(R). here I mean jacobson radical.

Prove that there is exactly one non-trivial twosided ideal,

namely

${f ∈ R| dimf (V ) < ∞} $ Prove that R is isomorphic to R + R here + means direct sum . thanks.

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

Join Physics Forums Today!

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

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

# Module homomorphism

Loading...

Similar Threads - Module homomorphism | Date |
---|---|

I Advantages of Vector Spaces over Modules | Aug 4, 2017 |

I Simple Modules and Right Annihilator Ideals ... | Feb 6, 2017 |

I Simple Modules and Maximal Right Ideals ... | Feb 4, 2017 |

(Apparently) simple question rearding module homomorphisms | May 9, 2014 |

Module Homomorphisms | Apr 7, 2005 |

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