Almost-free E(R)-algebras and E(A,R)-modules

Rüdiger Göbel, and Lutz Strüngmann. "Almost-free E(R)-algebras and E(A,R)-modules." Fundamenta Mathematicae 169.2 (2001): 175-192. <http://eudml.org/doc/281878>.

@article{RüdigerGöbel2001,
abstract = {Let R be a unital commutative ring and A a unital R-algebra. We introduce the category of E(A,R)-modules which is a natural extension of the category of E-modules. The properties of E(A,R)-modules are studied; in particular we consider the subclass of E(R)-algebras. This subclass is of special interest since it coincides with the class of E-rings in the case R = ℤ. Assuming diamond ⋄, almost-free E(R)-algebras of cardinality κ are constructed for any regular non-weakly compact cardinal κ > ℵ ₀ and suitable R. The set-theoretic hypothesis can be weakened.},
author = {Rüdiger Göbel, Lutz Strüngmann},
journal = {Fundamenta Mathematicae},
keywords = {-rings; -modules; diamond; weak diamond; endomorphism rings; almost-free algebras; almost-free modules; polynomial rings; torsion-free domains; regular cardinals},
language = {eng},
number = {2},
pages = {175-192},
title = {Almost-free E(R)-algebras and E(A,R)-modules},
url = {http://eudml.org/doc/281878},
volume = {169},
year = {2001},
}

TY - JOUR
AU - Rüdiger Göbel
AU - Lutz Strüngmann
TI - Almost-free E(R)-algebras and E(A,R)-modules
JO - Fundamenta Mathematicae
PY - 2001
VL - 169
IS - 2
SP - 175
EP - 192
AB - Let R be a unital commutative ring and A a unital R-algebra. We introduce the category of E(A,R)-modules which is a natural extension of the category of E-modules. The properties of E(A,R)-modules are studied; in particular we consider the subclass of E(R)-algebras. This subclass is of special interest since it coincides with the class of E-rings in the case R = ℤ. Assuming diamond ⋄, almost-free E(R)-algebras of cardinality κ are constructed for any regular non-weakly compact cardinal κ > ℵ ₀ and suitable R. The set-theoretic hypothesis can be weakened.
LA - eng
KW - -rings; -modules; diamond; weak diamond; endomorphism rings; almost-free algebras; almost-free modules; polynomial rings; torsion-free domains; regular cardinals
UR - http://eudml.org/doc/281878
ER -