caa a22 4500 386359814 CHVBK 20180307111911.0 cr unu---uuuuu 161130e198902 xx s 000 0 eng 10.1017/S0004972700027921 doi S0004972700027921 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700027921 Feigelstock Shalom Department of Math. and Computer Science, Bar-Ilan University, 52 100 Ramat-Gan, Israel Rings whose additive endomorphisms are N-multiplicative [Elektronische Daten] [Shalom Feigelstock] Sullivan's problem of describing rings, all of whose additive endomorphisms are multiplicative, is generalised to the study of rings R satisfying (a1 ... an) = (a1) (an) for every additive endomorphism of R, and all a1, ,an R, with n > 1 a fixed positive integer. It is shown that such rings possess a bounded (finite) ideal A such that [R/A]n = 0 ([R/A]2n−1 = 0). More generally, if f(X1, ..., Xt) is a homogeneous polynomial with integer coefficients, of degree > 1, and if a ring R satisfies [f(a1, ..., at)] = f[(a1), ..., (at)] for all additive endomorphisms , and all a1, ..., at R, then R possesses a bounded ideal A such that R/A satisfies the polynomial identity f. Copyright © Australian Mathematical Society 1989 Bulletin of the Australian Mathematical Society Cambridge University Press 39/1(1989-02), 11-14 0004-9727 39:1<11 1989 39 BAZ https://doi.org/10.1017/S0004972700027921 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700027921 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Feigelstock Shalom Department of Math. and Computer Science, Bar-Ilan University, 52 100 Ramat-Gan, Israel NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 39/1(1989-02), 11-14 0004-9727 39:1<11 1989 39 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence SWISSBIB 386359814 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge