# Representing the GCD as linear combination in non-PID rings

Kós, Géza
(2013)
*Representing the GCD as linear combination in non-PID rings.*
ACTA MATHEMATICA HUNGARICA, 140 (3).
pp. 243-247.
ISSN 0236-5294
MTMT:2385711; doi:10.1007/s10474-013-0314-z

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## Abstract

We prove the following fact: If finitely many elements p 1,p 2,...,p n of a unique factorization domain are given such that the greatest common divisor of each pair (p i,p j) can be expressed as a linear combination of p i and p j, then the greatest common divisor of all the p i's can also be expressed as a linear combination of p 1,...,p n. We prove an analogous statement in general commutative rings. © 2013 Akadémiai Kiadó, Budapest, Hungary.

Item Type: | ISI Article |
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Uncontrolled Keywords: | unique factorization domain, principal ideal, greatest common divisor |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

SWORD Depositor: | MTMT Injector |

Depositing User: | EPrints Admin |

Date Deposited: | 05 Feb 2014 12:32 |

Last Modified: | 05 Feb 2014 15:46 |

URI: | http://eprints.sztaki.hu/id/eprint/7538 |

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