## Abstract

In this paper, we study (Schelter) integral extensions of PI-rings. We prove in particular lying over, going up, and incomparability for prime ideals. A major result is transitivity of integrality: If R⊆S⊆B are PI-rings such that B is integral over S and S is integral over R, then B is integral over R. Next, we obtain a powerful criterion for integrality: If S is a prime PI-ring such that its center is integral over a Noetherian subring R of S, then S is integral over R. This allows interesting applications to the theory of finite group actions. Further topics concern Eakin-Nagata type results and embeddings of quotient rings for integral extensions. Finally, we analyze the relationship between module-finite extensions and finitely generated integral extensions, obtaining positive results for affine Noetherian PI-algebras and algebras satisfying certain restrictions on PI-degrees (e.g., algebras of low PI-degree).

Original language | English |
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Pages (from-to) | 39-79 |

Number of pages | 41 |

Journal | Journal of Algebra |

Volume | 151 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1992 |

### Bibliographical note

Funding Information:*This work was done while the first author enjoyedt he hospitalityo f the universityo f Southern California, Los Angeles. + Partially supported by NSF Grant DMS 8901491.

## ASJC Scopus subject areas

- Algebra and Number Theory