Rings whose additive endomorphisms are N-multiplicative

Shalom Feigelstock

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Sullivan's problem of describing rings, all of whose additive endomorphisms are multiplicative, is generalised to the study of rings R satisfying [formula ommited] for every additive endomorphism ϕ of R, and all a1,…,an ϵ R, with n > 1 a fixed positive integer. It is shown that such rings possess a bounded (finite) ideal A such that [formula ommited]. More generally, if f(X1, …, Xt) is a homogeneous polynomial with integer coefficients, of degree > 1, and if a ring R satisfies [formula ommited] for all additive endomorphisms ϕ, and all a1, …, at ϵ R, then R possesses a bounded ideal A such that R/A satisfies the polynomial identity f.

Original languageEnglish
Pages (from-to)11-14
Number of pages4
JournalBulletin of the Australian Mathematical Society
Issue number1
StatePublished - Feb 1989


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