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On Primitive Ideals in Polynomial Rings over Nil Rings

✍ Scribed by Agata Smoktunowicz

Publisher
Springer Netherlands
Year
2005
Tongue
English
Weight
158 KB
Volume
8
Category
Article
ISSN
1386-923X

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πŸ“œ SIMILAR VOLUMES

Polynomial Rings over Nil Rings Need Not
Polynomial Rings over Nil Rings Need Not Be Nil
✍ Agata Smoktunowicz πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 116 KB

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

Polynomial Rings over Nil Rings Cannot B
Polynomial Rings over Nil Rings Cannot Be Homomorphically Mapped onto Rings with Nonzero Idempotents
✍ K.I Beidar; Y Fong; E.R PuczyΕ‚owski πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 104 KB

We prove that the ring of polynomials in one indeterminate over a nil ring cannot be homomorphically mapped onto a ring containing a nonzero idempotent. This result can be regarded as an approximation of a positive solution of KΓΆthe's problem.