, Volume 25, Issue 1, pp 21-26

Rings whose additive endomorphisms aren-multiplicative, II

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Abstract

A ringR is called anAE n -ring,n≥2 a positive integer, if every endomorphism ϕ of additive group ofR satisfies ϕ(a 1 a 2...a n )=ϕ(a 1)ϕ(a 2)...ϕ(a n ) for alla 1,...,a n εR. Several results concerning the structure ofAE n -rings are obtained in this note, including an (incomplete) description ofAE n -ringsR satisfyingR t R n−1 ≠0, whereR t is the torsion ideal inR.