Self extending rings

S. Feigelstock

Research output: Contribution to journalArticlepeer-review

Abstract

A ring R is an IPQ (isomorphic proper quotient)-ring if R ≃ R/A for every proper ideal A ◁ R. If every ideal A ⊴ R satisfies: either R ≃ A or R ≃ R/A, then R is called an SE (self extending)-ring. It is shown that with one exception, an abelian group G is the additive group of an IPQ-ring if and only if G is the additive group of an SE-ring. The one exception is the infinite cyclic group Z. The zeroring with additive group Z is an SE-ring, but a ring with infinite cyclic additive group is not an IPQ-ring. Since the structure of the additive groups of IPQ-rings is known, the structure of the additive groups of SE-rings is completely determined.

Original languageEnglish
Pages (from-to)121-123
Number of pages3
JournalActa Mathematica Hungarica
Volume81
Issue number1-2
DOIs
StatePublished - Oct 1998

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