Titlebook: Basic Algebra; Anthony W. Knapp Textbook 2006 Birkhäuser Boston 2006 Group theory.Matrix.Multilinear Algebra.Vector space.algebra.linear a

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,Vector Spaces over ℚ, ℝ, and ℂ,up constructions of new vector spaces out of old ones, together with corresponding constructions for linear maps. The four constructions of vector spaces in these sections are those of the dual of a vector space, the quotient of two vector spaces, and the direct sum and direct product of two or more

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Multilinear Algebra,t leave some particular bilinear and Hermitian forms invariant..Section 6 introduces the tensor product of two vector spaces, working with it in a way that does not depend on a choice of basis. The tensor product has a universal mapping property—that bilinear functions on the product of the two vect

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Commutative Rings and Their Modules, with unique factorization, then so is the polynomial ring .[.]. This result is a consequence of Gauss’s Lemma, which addresses what happens to the greatest common divisor of the coefficients when one multiplies two members of .[.]. Gauss’s Lemma has several other consequences that relate factorizat

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Fields and Galois Theory,s..Section 3 classifies finite fields. For each integer . that is a power of some prime number, there exists one and only one finite field of order ., up to isomorphism. One finite field is an extension of another, apart from isomorphisms, if and only if the order of the first field is a power of th

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Modules over Noncommutative Rings,a composition series if and only if it satisfies both the ascending chain condition and the descending chain condition for its submodules..Sections 4–6 concern the Hom and tensor product functors. Section 4 regards Hom.(.), where . and . are unital left . modules, as a contravariant functor of the .