3 resultados para RESTRICTED LIE ALGEBRA

em DigitalCommons@University of Nebraska - Lincoln


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In January 1973, large numbers of Mugil cephalus (striped mullet), weighing approximately 250 gm each, died in two freshwater localities in tidewater bayous of Jackson County, Mississippi. Fish identified as Mugil curema, M. cephalus, Megalops atlantica, Dormitator maculatus, and Fundulus grandis were found dead in other low saline estuarine areas. Fish-kills during cold periods are less commonly encountered in Mississippi than in Texas or Florida. This particular incident is attributed to conditions of stress for fishes incompletely acclimated to the encountered low temperatures. The most deleterious stress was the low saline water which probably allowed a breakdown in the fishes' ion-osmoregulatory mechanisms. Striped mullet and other euryhaline fishes in salinities greater than 6 ppt survived, as did freshwater centrarchids and ictalurids in areas with dying mullet. Other stresses thought to contribute to the weakening of striped mullet in Paige Bayou during the period of rapidly decreasing temperatures include starvation and high levels of pesticide residues. In examined fish, the alimentary tracts were devoid of food, the gall bladders were distended and leaking bile, the livers contained excess lipid material and were often stained throughout with bile pigments, and the levels of DDT metabolites and endrin residues in the liver were higher than in control fish. Stress caused by low levels of dissolved oxygen, toxic substances in the water, or disease was discounted as a cause of death.

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Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.

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Topics include: Rings, ideals, algebraic sets and affine varieties, modules, localizations, tensor products, intersection multiplicities, primary decomposition, the Nullstellensatz