## Abstract

For any ring A, the group K_{1}A is filtered by the Whitehead determinants of invertible matrices over A of different sizes. We want to compute the corresponding graded group (especially the highest degree non-zero term) in terms of symbols which generalize Mennicke's symbol. In particular, we generalize the Bass-Milnor-Serre result which presents SK_{1}A of a Dedekind ring A via the Mennicke symbol, to an arbitrary commutative ring A satisfying the Bass second stable range condition. As an application, SK_{1}is computed for some rings of continuous functions. Some of our theorems are partially known, but we have often weakened hypotheses, using stable range conditions rather than Krull dimension (having in mind applications to rings of continuous functions).

Original language | English (US) |
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Pages (from-to) | 611-656 |

Number of pages | 46 |

Journal | Communications in Algebra |

Volume | 15 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1987 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory