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Polynomial Rings over Nil Rings Need Not Be Nil

✍ Scribed by Agata Smoktunowicz

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 116 KB
Volume: 233
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8451

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✦ Synopsis

We construct a nil algebra over a countable field, the polynomial ring over which is not nil. This answers a question of Amitsur.

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## Ž . I RESULT Let R be an associative ring. An element r g R is said to be nilpotent if r n s 0 for some integer n G 1. A subset S of R is called nil if all r g S are nilpotent. It is easy to see that R has no nil right ideals if and only if R has no nil left ideals. Nil right ideals or nil left