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
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
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 -