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.
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Feigelstock, S. Rings whose additive endomorphisms aren-multiplicative, II. Period Math Hung 25, 21–26 (1992). https://doi.org/10.1007/BF02454380
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DOI: https://doi.org/10.1007/BF02454380