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Poincaré duality algebras originated in the work of topologists on the cohomology of closed manifolds, and Macaulay's dual systems in the study of irreducible ideals in polynomial algebras. These two ideas are tied together using basic commutative algebra involving Gorenstein algebras. Steenrod operations also originated in algebraic topology, but may best be viewed as a means of encoding the information often hidden behind the Frobenius map in characteristic p<>0. They provide a noncommutative tool to study commutative algebras over a Galois field. In this Tract the authors skilfully bring together these ideas and apply them to problems in invariant theory. A number of remarkable and unexpected interdisciplinary connections are revealed that will interest researchers in the areas of commutative algebra, invariant theory or algebraic topology.
Duality theory (Mathematics) --- Steenrod algebra --- Poincaré series --- Poincaré series. --- Steenrod algebra. --- Algebra, Steenrod --- Algebraic topology --- Algebra --- Mathematical analysis --- Topology --- Series, Poincaré
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Verzorging-Voeding --- 3e graad secundair onderwijs --- Promotie --- Lerarenopleiding --- Bachelor in het onderwijs : secundair onderwijs --- Voeding-Verzorging --- h.o.
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Verzorging-Voeding --- 3e graad secundair onderwijs --- Promotie --- Lerarenopleiding
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In unserer hochtechnisierten Welt verschwimmen die Grenzen zwischen Mensch und Maschine in zahlreichen Bereichen der Wissenschaft, der Arbeit und des Alltagslebens immer mehr. Diese Verflechtungen beeinflussen unser tägliches Leben und stellen Möglichkeiten, aber auch Einschränkungen, Chancen und Herausforderungen dar. Die Beiträge des Bandes greifen diese Themen auf, indem sie eine stark interdisziplinäre Perspektive einnehmen. Wie wirken sich Digitalisierung und Künstliche Intelligenz in der Lebens- und Arbeitswelt auf die Geschlechterverhältnisse aus? Wie kann Intersektionalität in einer zunehmend international vernetzten Welt neu verstanden werden? In numerous fields of science, work, and everyday life, humans and machines have been increasingly entangled, developing an ever-growing toolbox of interactions. These entanglements affect our daily lives and pose possibilities as well as restrictions, chances as well as challenges. The contributions of this volume tackle related issues by adopting a highly interdisciplinary perspective. How do digitalization and artificial intelligence affect gender relations? How can intersectionality be newly understood in an increasingly internationally networked world? This volume is a collection of contributions deriving from the "Interdisciplinary Conference on the Relations of Humans, Machines and Gender" which took place in Braunschweig (October 16-19, 2019). It also includes the keynotes given by Cecile Crutzen, Galit Wellner and Helen Verran.
artificial intelligence --- Digitalisierung --- digitalization --- gender relations --- gender studies --- Geschlechterforschung --- Geschlechterverhältnisse --- human-machine interaction --- interdisciplinarity --- Interdisziplinarität --- Künstliche Intelligenz --- Mensch-Maschine-Interaktion --- science and technology studies --- Technikforschung
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