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ERIC Number: EJ1138704
Record Type: Journal
Publication Date: 2017
Pages: 8
Abstractor: As Provided
Reference Count: 6
ISBN: N/A
ISSN: ISSN-0020-739X
The Rings with Identity Whose Additive Subgroups Are One-Sided Ideals
Dobbs, David E.
International Journal of Mathematical Education in Science and Technology, v48 n5 p774-781 2017
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}, Z/pZ 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}, Z, Z/nZ 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.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A