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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