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 $R={\mathbb Z}$. Assuming diamond
$\diamond $, almost-free $E(R)$-algebras of cardinality $\kappa
$ are constructed for any regular non-weakly compact cardinal
$\kappa > \aleph _0$ and suitable $R$. The set-theoretic
hypothesis can be weakened.
Keywords:
unital commutative ring unital r algebra introduce category modules which natural extension category e modules properties modules studied particular consider subclass algebras subclass special interest since coincides class e rings mathbb assuming diamond diamond almost free algebras cardinality kappa constructed regular non weakly compact cardinal kappa aleph suitable set theoretic hypothesis weakened
Affiliations des auteurs :
Rüdiger Göbel
1
;
Lutz Strüngmann
1
1
Fachbereich 6, Mathematik und Informatik Universität Essen 45117 Essen, Germany
@article{10_4064_fm169_2_6,
author = {R\"udiger G\"obel and Lutz Str\"ungmann},
title = {Almost-free $E(R)$-algebras and $E(A,R)$-modules},
journal = {Fundamenta Mathematicae},
pages = {175--192},
year = {2001},
volume = {169},
number = {2},
doi = {10.4064/fm169-2-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm169-2-6/}
}
TY - JOUR
AU - Rüdiger Göbel
AU - Lutz Strüngmann
TI - Almost-free $E(R)$-algebras and $E(A,R)$-modules
JO - Fundamenta Mathematicae
PY - 2001
SP - 175
EP - 192
VL - 169
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4064/fm169-2-6/
DO - 10.4064/fm169-2-6
LA - en
ID - 10_4064_fm169_2_6
ER -
