## Abstract

Let D be an integral domain, D[X] be the polynomial ring over D, and w be the so-called w-operation on D. We define D to be a w-LPI domain if every nonzero w-locally principal ideal of D is w-invertible. This article presents some properties of w-LPI domains. It is shown that D is a w-LPI domain if and only if D[X] is a w-LPI domain, if and only if D[X]_{Nv}is an LPI domain, where N_{v}= {f ∈ D[X] {pipe} c(f)^{-1}= D}. As a corollary, it is also shown that D is a w-LPI domain if and only if each w-locally finitely generated and w-locally free submodule of D^{n}of rank n over D is of w-finite type. We show that if D = ∩_{α} D_{α} is a finite character intersection of t-linked overrings D_{α} and if each D_{α} is a w-LPI domain, then D is a w-LPI domain.

Original language | English |
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Pages (from-to) | 3805-3819 |

Number of pages | 15 |

Journal | Communications in Algebra |

Volume | 41 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2013 |

## Keywords

- t-invertible
- t-Nagata ring
- w-Faithfully flat
- w-Flat
- w-LPI domain