Notes on Ring Theory |
Common terms and phrases
2-sided algebra of G algebra of linear algebra over F algebraic algebra Amer central simple centroid condition on right contains Definition dense ring density theorem descending chain condition dimension dimensional direct sum division algebra division ring dual vector spaces endomorphisms F has characteristic field F finite number full dual group algebra group G Hence idempotent integer irreducible right A-module isomorphic L's and R's left vector space Lemma linear transformations linearly independent locally finite mapping Math matrix ring maximal right ideal minimal left ideal multiplication nilpotent ideals non-zero element polynomial identity primitive ring radical ideal radical ring Regular ideal regular maximal right Regular ring Remark representation right primitive ideals right primitive ring right quasi-regular ring of linear satisfies the descending semi-group semi-simple simple ring subalgebra subgroup submodules Suppose Theorem 16 torsion group total matrix algebra trivial two-ideal unit element