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Sheaves of Algebras over Boolean Spaces comprehensively covers sheaf theory as applied to universal algebra. Sheaves decompose general algebras into simpler pieces called the stalks. A classical case is commutative von Neumann regular rings, whose stalks are fields. Other classical theorems also extend to shells, a common generalization of rings and lattices. This text presents intuitive ideas from topology such as the notion of metric space and the concept of central idempotent from ring theory. These lead to the abstract notions of complex and factor element, respectively. Factor elements are defined by identities, discovered for shells for the first time, explaining why central elements in rings and lattices have their particular form. Categorical formulations of the many representations by sheaves begin with adjunctions and move to equivalences as the book progresses, generalizing Stone’s theorem for Boolean algebras. Half of the theorems provided in the text are new; the rest are presented in a coherent framework, starting with the most general, and proceeding to specific applications. Many open problems and research areas are outlined, including a final chapter summarizing applications of sheaves in diverse fields that were not covered earlier in the book. This monograph is suitable for graduate students and researchers, and it will serve as an excellent reference text for those who wish to learn about sheaves of algebras.

Algebra, Boolean. --- Sheaf theory. --- Algebra, Boolean --- Sheaf theory --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematical Theory --- Topological spaces. --- Spaces, Topological --- Cohomology, Sheaf --- Sheaf cohomology --- Sheaves, Theory of --- Sheaves (Algebraic topology) --- Boolean algebra --- Boole's algebra --- Mathematics. --- Algebra. --- Category theory (Mathematics). --- Homological algebra. --- Topology. --- Category Theory, Homological Algebra. --- Algebraic topology --- Algebraic logic --- Set theory --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Algebras, Linear --- Mathematical analysis --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory

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Algebra, Universal --- Lattice theory --- Varieties (Universal algebra)

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Mathematical analysis --- analyse (wiskunde) --- wiskunde --- Calcul infinitésimal --- Calcul infinitesimal --- Calcul infinitesimal - Problèmes et exercices

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Experience the discovery of mathematics by reading the original work of some of the greatest minds throughout history. Here are the stories of four mathematical adventures, including the Bernoulli numbers as the passage between discrete and continuous phenomena, the search for numerical solutions to equations throughout time, the discovery of curvature and geometric space, and the quest for patterns in prime numbers. Each story is told through the words of the pioneers of mathematical thought. Particular advantages of the historical approach include providing context to mathematical inquiry, perspective to proposed conceptual solutions, and a glimpse into the direction research has taken. The text is ideal for an undergraduate seminar, independent reading, or a capstone course, and offers a wealth of student exercises with a prerequisite of at most multivariable calculus.

Number theory --- Differential geometry. Global analysis --- Mathematics --- Computer science --- differentiaal geometrie --- geschiedenis --- wiskunde --- algoritmen --- getallenleer