Title: Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
Subjects: Mathematics, Polynomial rings, PI-algebras, Representations of algebras, Associative rings and algebras {For the commutative case, see 13-XX} -- Algebras and orders {For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30} -- Separable algebra, Associative rings and algebras {For the commutative case, see 13-XX} -- Rings with polynomial identity -- $T$-ideals, identities, varieties of rings and algebras, Associative rings and algebras {For the commutative case, see 13-XX} -- Rings with polynomial identity -- Semiprime p.i. rings, rings embeddable in matrices over commutative rings, Associative rings and algebras {For the commutative case, see 13-XX} -- Rings with polynomial identity -- Trace rings and invariant theory, Associative rings and algebras {For the commutative case, see 13-XX} -- Rings and algebras with additional structure -- Actions of groups and semigroups; invariant theory, Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Exterior algebra, Grassmann algebras, Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Vector and tensor algebra, theory of invariants [See also 13A50, 14L24], Algebraic geometry -- Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45} -- Geometric invariant theory [See also 13A50], Associative rings and algebras {For the commutative case, see 13-XX} -- Radicals and radical properties of rings -- Prime and semiprime rings [See also 16D60, 16U10], Associative rings and algebras {For the commutative case, see 13-XX} -- Chain conditions, growth conditions, and other forms of finiteness -- Growth rate, Gelfand-Kirillov dimension