### Abstract

We shall prove a version of Gauß's lemma. It works in Z[a,A, b,B] where a = {a_{i}}^{m} _{i=0}, A = {A_{i}}^{m} _{i=0}, b = {b_{i}}^{n} _{j=0}, B = {B_{j}}^{n} _{j=0}, and constructs polynomials {c_{k}}k=0,... ,m+n of degree at most in each variable set a,A, b,B, with this property: setting for elements a_{i},A_{j}, b_{j}, B_{j} in any commutative ring R satisfying, the elements ck = c_{k}(a_{i},A_{i}, b_{j},B_{j}) satisfy.

Original language | English (US) |
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Pages (from-to) | 299-307 |

Number of pages | 9 |

Journal | Journal of Commutative Algebra |

Volume | 5 |

Issue number | 2 |

DOIs | |

State | Published - 2013 |

### Keywords

- Constructive
- Gauss lemma

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## Cite this

Messing, W., & Reiner, V. (2013). A universal coefficient theorem for gauss's lemma.

*Journal of Commutative Algebra*,*5*(2), 299-307. https://doi.org/10.1216/JCA-2013-5-2-299