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A-Rings

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Dugas M., Feigelstock S.

Colloquium Mathematicum

2003

tom 96

nr 2

277-292

A ring R is called an E-ring if every endomorphism of R⁺, the additive group of R, is multiplication on the left by an element of R. This is a well known notion in the theory of abelian groups. We want to change the "E" as in endomorphisms to an "A" as in automorphisms: We define a ring to be an A-ring if every automorphism of R⁺ is multiplication on the left by some element of R. We show that many torsion-free finite rank (tffr) A-rings are actually E-rings. While we have an example of a mixed A-ring that is not an E-ring, it is still open if there are any tffr A-rings that are not E-rings. We will employ the Strong Black Box [5] to construct large integral domains that are A-rings but not E-rings.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Dugas M.

1 Feigelstock S.

1 2003

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A-Rings