TY - JOUR

T1 - Self extending rings

AU - Feigelstock, S.

PY - 1998/10

Y1 - 1998/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032221373&partnerID=8YFLogxK

U2 - 10.1023/a:1006527213504

DO - 10.1023/a:1006527213504

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AN - SCOPUS:0032221373

SN - 0236-5294

VL - 81

SP - 121

EP - 123

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1-2

ER -