## Abstract

Isomorphisms of general linear groups over associative rings graded by a commutative is studied by a general theorem. The description of isomorphisms of the groups of invertible elements of endomorphism rings over free graded modules over associative rings graded by a commutative group is found. Two associative rings, R and S and group isomorphism are considered. It is found that there exist central idempotents e and f of the two rings, a ring isomorphism and a ring antiisomorphism. A ring is called G-graded if it is a system of additive subgroups of the ring R. For a commutative group with associative graded rings are graded matrix rings, there exists a group isomorphism.

Original language | English |
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Pages (from-to) | 175-176 |

Number of pages | 2 |

Journal | Doklady Mathematics |

Volume | 83 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2011 |

Externally published | Yes |