Two-Sided Ideals in Rings of Differential Operators and Étale Homomorphisms

✍ Scribed by G. Masson

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 429 KB
• Volume: 171
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1995.1035

✦ Synopsis

Let (A) be a commutative Noetherian and reduced ring. If (A) has an étale covering (B) such that all the irreducible components of (B) are geometric unibranches, we will construct an invariant ideal (\gamma(A)) of (A) which has the following properties: If (A) is an algebra over some ring (k), then (\gamma(A)) is an essential left (C(A))-submodule of (A), and if all the irreducible components of (B) have rings of differential operators that are simple, then (\gamma(A)) is the minimal essential left (\partial(A))-submodule of (A), and (\mathscr{D}(A, \gamma(A))) is the minimal essential two-sided ideal of (\mathscr{P}(A)). 1945 Academic Press, Inc.