## PI-algebras: an introduction |

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### Contents

INTRODUCTION | 1 |

Two results on the radical | 7 |

Formal results | 15 |

Copyright | |

12 other sections not shown

### Common terms and phrases

algebra of linear algebraically closed Amitsur Artinian assume automorphism called central division algebra central polynomial central simple algebra coefficients commutative ring contains cyclic algebra cyclic group defined denote dimensional central simple division algebra exists extension field finite dimensional central follows Galois group Hence idempotents identity f identity of degree implies infinite field invertible irreducible isomorphism K-algebra K-module K{xj Laurent series left ideal LEMMA Let f linear transformations linearly independent locally nilpotent lower nil radical matrix units maximal ideal maximal subfield minimum polynomial Mn(K module monoid monomials multilinear multiplication nil ideal nilpotent ideal non-zero element obtain open subset polynomial function prime algebras satisfying prime ideal primitive Proof prove residue field result roots satisfying a proper semi-prime semi-primitive shows splitting field strongly regular identity subalgebra submodule suppose T-ideal THEOREM UD(K universal PI-algebra upper nil radical vector space