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Rings of Operators on Modules over Commutative Rings and Their Right Ideals

✍ Scribed by R.C Cannings; M.P Holland

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 300 KB
Volume: 186
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0371

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✦ Synopsis

We introduce and impose conditions under which the finitely generated essential right ideals of E may be classified in terms of k-submodules of M. This yields a classification of the domains Morita equivalent to E when E is a Noetherian domain. For example, a special case of our results is:

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ww xx Let k be an algebraically closed field of characteristic zero, O O s k x , . . . , x n 1 n the ring of formal power series over k, and D D the ring of differential operators n over O O . Suppose that is a prime ideal of O O of height n y 1; i.e., A s O O r is a n n n curve. We prove that every