TABLE OF CONTENTS
1. Preliminaries 6
2. Global Subdirect Products 11
3. TheHull-Kernel Topology 32
U. Patching *+3
5. Closure under theNormal Transform 66
6. Globally Representable Varieties 81
7. Global Subdirect Representation ofRings 89
8. Global Subdirect Representation of Lattice Ordered Rings 100
ABSTRACT
An internal characterization is given of those subdirect products
which are structures of global sections of discrete sheaves. Such subdirect
products are called global. Patching of subdirect products over a dual ring
of subsets of the index set is defined, and a uniform method of constructing
global subdirect products from the patching property is developed. The role
of the hull-kernel topology in sheaf constructions is analysed in the
setting of universal algebra. Global subdirect products which come from
Hausdorff sheaves over Boolean spaces (Boolean subdirect products) are treated
in terms of the normal transform. Global representation of varieties is
defined and investigated. Finally, applications to the sheaf representation
of rings and lattice ordered rings are given.
AMS (MPS) subject classifications(1970) : Primary 08A0^,
08A25. Secondary 08A15,16A^8,06A70.
Key words and phrases : Sheaf representation, patchwork property,
equalizer topology, hull-kernel topology, structure of global sections,
Boolean subdirect product, normal transform, representation of varieties, semi-
prime rings, biregular rings, Baer rings, lattice-ordered rings, function
rings.
Library of Coagraaa CataJogiaf ia Publication Data
Krauss, Peter H., 1933-
Global subdirect products.
ODE
(Memoirs of the American Mathematical Society ;
no. 210)
Bibliography: p.
1. Algebra, Universal. 2. Associative rings.
3. Sheaves, Theory of. I
joint author. II. Title.
Clark, David M., 19^7-
III. Series: American
Mathematical Society. Memoirs ; no. 210.
QA3.A57 no. 210 [QA251] 510'.8s [512] 78-23373
ISBN 0-8218-2210-1
Copyright © 1979, American Mathematical Society
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