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ABSTRACT Let R be a ring with identity. Then {0} and R are the only additive subgroups of R if and only if R is isomorphic (as a ring with… Click to show full abstract
ABSTRACT Let R be a ring with identity. Then {0} and R are the only additive subgroups of R if and only if R is isomorphic (as a ring with identity) to (exactly) one of {0}, for a prime number p. Also, each additive subgroup of R is a one-sided ideal of R if and only if R is 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.
Keywords:
rings identity;
one sided;
additive subgroups;
whose additive;
identity;
identity whose
Journal Title: International Journal of Mathematical Education in Science and Technology
Year Published: 2017
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Journal Title: International Journal of Mathematical Education in Science and Technology
Year Published: 2017
Link to full text (if available)
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recommendations!