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This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.
Contains data and actual salaries on over 9,000 Federal civil service leadership and support positions in the legislative and executive branches of the Federal government that may be subject to noncompetitive appointments.
This proceedings is composed of the papers resulting from the NATO work-shop "Perspectives in Ring Theory" and the work-shop "Geometry and Invariant The ory of Representations of Quivers" . Three reports on problem sessions have been induced in the part corresponding to the work-shop where they belonged. One more report on a problem session, the "lost" problem session, will be published elsewhere eventually. vii Acknowledgement The meeting became possible by the financial support of the Scientific Affairs Division of NATO. The people at this division have been very helpful in the orga nization of the meeting, in particular we commemorate Dr. Mario di Lullo, who died unexpectedly last year, b...
A pictoral history of Willow Run - a relative unknown location that became the world's most famous bomber factory during World War II. In May 1940, Pres. Franklin D. Roosevelt called for the production of 50,000 military airplanes. He then drafted the president of General Motors, William Knudsen, to mobilize industry in the United States. The automotive companies were called upon to produce a massive fleet of bombers, as well as tanks, trucks, guns, and engines. By the Willow Run, a sleepy little creek near Ypsilanti, Michigan, Ford Motor Company built the world's most famous bomber factory, which was the ultimate manifestation of the automotive industry's role in building armaments during World War II. By the spring of 1944, Willow Run was producing a four-engine B-24 bomber each hour on an assembly line.
Dive into the heart of wartime innovation and manufacturing through this groundbreaking book, unveiling a riveting narrative of technological mastery and organizational ingenuity. This meticulously researched work challenges conventional views of wartime production, offering a fresh perspective on the incredible efforts that drove the Allies to victory. Young's insightful analyses illuminate the strategic collaboration between the aerospace and automotive industries, showcasing their collective adaptation that created the engines powering victory. Spanning continents, Young examines the transformation of aircraft engine manufacturing during World War II. Unearthing the operations of key play...
Covers receipts and expenditures of appropriations and other funds.