TY - JOUR

T1 - Rings whose additive endomorphisms are N-multiplicative

AU - Feigelstock, Shalom

PY - 1989/2

Y1 - 1989/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77950649968&partnerID=8YFLogxK

U2 - 10.1017/S0004972700027921

DO - 10.1017/S0004972700027921

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AN - SCOPUS:77950649968

SN - 0004-9727

VL - 39

SP - 11

EP - 14

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 1

ER -