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Regularity in terms of reductions in local Noether lattices


Author: Michael E. Detlefsen
Journal: Proc. Amer. Math. Soc. 43 (1974), 1-7
MSC: Primary 13A15
DOI: https://doi.org/10.1090/S0002-9939-1974-0327728-0
MathSciNet review: 0327728
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Abstract: An $ (n,d)$-sequence in a local Noether lattice $ (L,M)$ is a sequence of words which satisfy certain factorization properties. If $ (L,M)$ satisfies the union condition, there exist $ (n,d)$-sequences which can be extended to minimal bases for the powers of $ M$. Consequently, if $ (L,M)$ satisfies the union condition, $ (L,M)$ is regular if and only if $ M$ is a minimal reduction.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0327728-0
Keywords: Regular local Noether lattice, free monoid, reduction, union condition, analytically independent, $ (n,d)$-sequence
Article copyright: © Copyright 1974 American Mathematical Society

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