Regularity in terms of reductions in local Noether lattices

Detlefsen, Michael E.

doi:10.1090/S0002-9939-1974-0327728-0

Regularity in terms of reductions in local Noether lattices
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by Michael E. Detlefsen

Proc. Amer. Math. Soc. 43 (1974), 1-7

DOI: https://doi.org/10.1090/S0002-9939-1974-0327728-0

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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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