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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Boundedness versus periodicity over commutative local rings

Authors: Vesselin N. Gasharov and Irena V. Peeva
Journal: Trans. Amer. Math. Soc. 320 (1990), 569-580
MSC: Primary 13D05; Secondary 13H99
MathSciNet review: 967311
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Abstract: Over commutative graded local artinian rings, examples are constructed of periodic modules of arbitrary minimal period and modules with bounded Betti numbers, which are not eventually periodic. They provide counterexamples to a conjecture of D. Eisenbud, that every module with bounded Betti numbers over a commutative local ring is eventually periodic of period $ 2$. It is proved however, that the conjecture holds over rings of small length.

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Keywords: Betti numbers, periodic module, minimal free resolution
Article copyright: © Copyright 1990 American Mathematical Society