Algebra I: Basic Notions of Algebra |
Common terms and phrases
a₁ Abelian groups algebraic groups algebras of finite analogue arbitrary automorphism axioms called coefficients cohomology commutative ring compact complex analytic complex numbers consider consists construction contained coordinate coordinatisation corresponding coset curve defined definition denoted differential operators dimension direct sum division algebra e₁ elements equation exact sequence Example exists extension L/K F₂ finite groups finite number finite rank finite type finite-dimensional follows functor G₁ G₂ Galois geometry given GL(n group G Hence homomorphism identity integral invariant inverse irreducible representations isomorphic kernel lattice Lie algebra Lie groups linear transformations manifold matrix module morphisms multiplication n-dimensional Noetherian normal subgroup notion number field Obviously p₁ permutations plane properties proved quaternions quotient rational functions real number relations satisfying semisimple sheaf simple SL(n solvable submodule subspace symmetry group tensor Theorem theory topological space unique vector fields vector space