Envelopes of commutative rings

  1. Parra, Rafael
  2. Saorín Castaño, Manuel
Zeitschrift:
Notas de matemática

ISSN: 1856-7800

Datum der Publikation: 2009

Ausgabe: 5

Nummer: 1

Seiten: 13-38

Art: Artikel

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Zusammenfassung

Given a significative class F of commutative rings, we study the precise conditions under which a commutative ring R has an F-envelope. A full answer is obtained when F is the class of fields, semisimple commutative rings or integral domains. When F is the class of Noetherian rings, we give a full answer when the Krull dimension of R is zero and when the envelope is required to be epimorphic. The general problem is reduced to identifying the class of non-Noetherian rings having a monomorphic Noetherian envelope, which we conjecture is the empty class.

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