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

Rüdiger Göbel; Lutz Strüngmann

Fundamenta Mathematicae (2001)

- Volume: 169, Issue: 2, page 175-192
- ISSN: 0016-2736

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topRüdiger 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 -

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