Topics in algebra

Publication date 1975 Topics Algebra, Algèbre, algebra, Algebra, Abstract Publisher New York : Wiley Collection internetarchivebooks; printdisabled Contributor Internet Archive Language English Item Size 1.2G

xi, 388 pages ; 24 cm

Includes bibliographical references and index

Preliminary notions : Set theory ; Mappings ; The integers -- Group theory : Definition of a group ; Some examples of groups ; Some preliminary lemmas ; Subgroups ; A counting principle ; Normal subgroups and quotient groups ; Homomorphisms ; Automorphisms ; Cayley’s Theorem ; Permutation groups ; Another counting principle ; Sylow’s theorem ; Direct products ; Finite abelian groups -- Ring theory : Definition and examples of rings ; Some special classes of rings ; Homomorphisms ; Ideals and quotient rings ; The field of quotients of an integral domain ; Euclidean rings ; A particular Euclidean ring ; Polynomial rings ; Polynomial over the rational field ; Polynomial rings over commutative rings -- Vector spaces and modules : Elementary basic concepts ; Linear independence and bases ; Dual spaces ; Inner product spaces ; Modules -- Fields : Extension fields ; The transcendence of e ; Roots of polynomials ; Construction with straightedge and compass ; More about roots ; The elements of Galois theory ; Solvability by radicals ; Galois groups over the rationales -- Linear transformations : The algebra of linear transformations ; Characteristic roots ; Matrices ; Canonical forms: triangular form ; Canonical forms: nilpotent transformations ; Canonical forms: a decomposition of V: Jordan form ; Canonical forms: rational canonical form ; Trace and transpose ; Determinants ; Hermitian, unitary, and normal transformations ; Real quadratic forms -- Selected topics : Finite fields ; Wedderburn’s theorem on finite division rings ; A theorem of Frobenius ; Integral quaternions and the four-square theorem

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