Resumen de The rings with identity whose additive subgroups are one-sided ideals

David E. Dobbs

• Let Rbe a ring with identity. Then {0} and Rare the only additive subgroups of Rif and only if Ris isomorphic (as a ring with identity) to (exactly) one of {0}, for a prime number p. Also, each additive subgroup of Ris a one-sided ideal of Rif and only if Ris isomorphic to (exactly) one of {0}, , for an integer n= 2. This note could find classroom use in a first course on abstract algebra as enrichment material for the unit on ring theory.