A-Rings

• Autorzy: Manfred Dugas , Shalom Feigelstock
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20K30: Automorphisms, homomorphisms, endomorphisms, etc.
• 20K20: Torsion-free groups, infinite rank
• 20K15: Torsion-free groups, finite rank

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 96
• Numer: 2
• Strony: 277-292

Daty

wydano

2003

Twórcy

autor

Manfred Dugas

• Department of Mathematics, Baylor University, Waco, Texas 76798, U.S.A.

autor

Shalom Feigelstock

• Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel

Identyfikatory

DOI

10.4064/cm96-2-10