Galois Theory (eBook)

Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures,

Emil Artin (Autor)

Arthur N. Milgram (Herausgeber)

eBook Download: EPUB

2012
86 Seiten
Dover Publications (Verlag)
978-0-486-15825-9 (ISBN)

Infos

Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.

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In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications.The first section deals with linear algebra, including fields, vector spaces, homogeneous linear equations, determinants, and other topics. A second section considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equations, Jummer's fields, and more.Dr. Milgram's section on applications discusses solvable groups, permutation groups, solution of equations by radicals, and other concepts.

Inhalt

I. Linear Algebra A. Fields B. Vector Spaces C. Homogeneous Linear Equations D. Dependence and Independence of Vectors E. Non-homogeneous Linear Equations F. DeterminantsII. Field Theory A. Extension fields B. Polynomials C. Algebraic Elements D. Splitting fields E. Unique Decomposition of Polynomials into Irreducible Factors F. Group Characters G. Applications and Examples to Theorem 13 H. Normal Extensions I. Finite Fields J. Roots of Unity K. Noether Equations L. Kimmer's Fields M. Simple Extensions N. Existence of a Normal Basis O. Theorem on natural IrrationalitiesIII. Applications. By A. N. Milgram A. Solvable Groups B. Permutation Groups C. Solution of Equations by Radicals D. The General Equation of Degree n E. Solvable Equations of Prime Degree F. Ruler and Compass Construction

Produkt-Details

• Erscheint lt. Verlag: 24.5.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 113 g
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: abstract algebra • advanced math • algebra class • Algebraic • Algebras • algebra text • Algebra Textbook • Applications • artin • books on abstract algebras • books on advanced maths • books on algebra classes • books on algebras • books on algebra textbooks • books on algebra texts • books on applications • books on equations • books on evariste • books on exercises • books on factorizations • books on fields • books on foote • books on hungerford • books on ivory towers • books on jacobson • books on kummer • books on lemma • books on level maths • books on linear algebras • books on mathematical objects • books on mathematicians • books on mathematics • books on math texts • books on permutations • books on pinter • books on polynomials • books on proofs • books on properties • books on quotients • books on radicals • books on self studies • books on self-studies • books on strang • books on tensors • books on theorems • books on undergrads • carefully explained • Equations • evariste • Exercises • Factorization • Fields • foote • gamma function • highly disorganized • Hungerford • ivory tower • Jacobson • join • Joining • Kummer • Lemma • level math • linear algebra • mathematical objects • Mathematicians • Mathematics • math text • Noether • Permutation • Pinter • polynomials • proofs • Properties • Quotient • Radicals • Rigorous • self study • Self-study • solvability • solvable • strang • Symmetric • Tensors • Theorems • undergrad • undergraduate
• ISBN-10: 0-486-15825-X / 048615825X
• ISBN-13: 978-0-486-15825-9 / 9780486158259