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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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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Keywords: Regular local Noether lattice, free monoid, reduction, union condition, analytically independent, <IMG WIDTH="53" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$(n,d)$">-sequence
Article copyright: © Copyright 1974 American Mathematical Society