A-Rings

Manfred Dugas, and Shalom Feigelstock. "A-Rings." Colloquium Mathematicae 96.2 (2003): 277-292. <http://eudml.org/doc/284459>.

@article{ManfredDugas2003,
abstract = {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.},
author = {Manfred Dugas, Shalom Feigelstock},
journal = {Colloquium Mathematicae},
keywords = {-rings; -rings; black box; endomorphisms; automorphisms; left multiplications},
language = {eng},
number = {2},
pages = {277-292},
title = {A-Rings},
url = {http://eudml.org/doc/284459},
volume = {96},
year = {2003},
}

TY - JOUR
AU - Manfred Dugas
AU - Shalom Feigelstock
TI - A-Rings
JO - Colloquium Mathematicae
PY - 2003
VL - 96
IS - 2
SP - 277
EP - 292
AB - 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.
LA - eng
KW - -rings; -rings; black box; endomorphisms; automorphisms; left multiplications
UR - http://eudml.org/doc/284459
ER -