Almost-free $E(R)$-algebras and $E(A,R)$-modules
Volume 169 / 2001
Fundamenta Mathematicae 169 (2001), 175-192
MSC: 20K20, 20K30, 16W20.
DOI: 10.4064/fm169-2-6
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 $R={\mathbb Z}$. 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.
