Fundamental concepts of algebra: Fundamental Concepts of Algebra

additive group Assume automorphism bijection bilinear called commutative ring contains corollary coset defined denote derivation of degree direct sum elements of degree endomorphism epimorphism exists a unique exterior algebra family of elements finite number following conditions follows immediately form a base formula free module graded algebra group G homo homogeneous elements homogeneous of degree homomorphism f identity mapping integers invertible isomorphism kernel law of composition left module lemma Let f Let Q linear combination linear form linear mapping mapping f module of homogeneous monomorphism morphism multilinear mapping natural mapping necessary and sufficient neutral element normal subgroup notation permutation polynomial quotient monoid resp right module Sect set of elements Show strictly increasing sequence subalgebra subgroup of G submodule submonoid subset subspace symmetric algebra tensor product theorem 17 unique homomorphism unit element vector space whence