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.
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {167},
year = {2001},
pages = {175-192},
zbl = {0991.20040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-2-6}
}
Rüdiger Göbel; Lutz Strüngmann. Almost-free E(R)-algebras and E(A,R)-modules. Fundamenta Mathematicae, Tome 167 (2001) pp. 175-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-2-6/