### Abstract

Let R = k[[x_{0},...,x_{d}]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x_{0},...,x_{d}]]. We investigate the question of which rings of this form have bounded Cohen-Macaulay type, that is, have a bound on the multiplicities of the indecomposable maximal Cohen-Macaulay modules. As with finite Cohen-Macaulay type, if the characteristic is different from two, the question reduces to the one-dimensional case: The ring R has bounded Cohen-Macaulay type if and only if R≅k[[x_{0},...,x_{d}]]/ (g+x_{2}
^{2} + ⋯ + x_{d}
^{2}), where g ∈ k[[x_{0}, x_{1}]] and k[[x_{0}, x_{1}]]/(g) has bounded Cohen-Macaulay type. We determine which rings of the form k[[x_{0}, x _{1}]]/(g) have bounded Cohen-Macaulay type.

Original language | English (US) |
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Pages (from-to) | 204-217 |

Number of pages | 14 |

Journal | Journal of Pure and Applied Algebra |

Volume | 201 |

Issue number | 1-3 |

DOIs | |

State | Published - Oct 1 2005 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Pure and Applied Algebra*,

*201*(1-3), 204-217. https://doi.org/10.1016/j.jpaa.2004.12.028