## Notes on ring theory |

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### Contents

The Radical | 2 |

Frimitive Rings and the Density Theorem | 11 |

SemiSimple Rings | 26 |

4 other sections not shown

### Common terms and phrases

2-ideal 2-sided algebra of G algebra of linear algebra over F algebraic algebra Amer automorphism central simple centroid commutative condition on right contains Definition dense ring descending chain condition dimension direct sum division algebra division ring endomorphisms F has characteristic faithful irreducible right field F finite number full dual G is locally group algebra group G Hence hypothesis idempotent integer irreducible right A-module isomorphic Lemma linear transformations linearly independent locally finite mapping Math matrix ring maximal right ideal maximal subfield minimal left ideal nilpotent ideals non-zero element orthogonal polynomial identity primitive ideals primitive ring radical ideal radical ring Regular ideal regular maximal right Regular ring Remark representation right primitive ideal right primitive ring right quasi-regular ring of linear satisfies the descending semi-group semi-simple simple ring subalgebra subgroup submodules Suppose Theorem 16 topological torsion group total matrix algebra trivial two-ideal unit element zero