T-Ideals and C-Ideals
Copyright policy )T-Ideals and C-Ideals
Given a ring R we consider the category Ŕ of R-rings (rings A with given ring-homomorphisms R → A), and R-homomorphisms (ring-homomorphisms that form commutative triangles with the given maps from R). All rings are associative and have 1, all homomorphisms send 1 to 1.We define a c-R-ring as an object A in Ŕ with a family of maps {ρx ∈ homŔ(A,A)|x∈A}. Equivalently, a c-R-ring is an R-ring A with a binary operation a · b(= aρb) on A satisfying
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Category-theoretic methods and results in associative algebras (except as in 16D90), free algebras, Rings with polynomial identity, c-ideal, T-ideals, category of c-R-rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
Category-theoretic methods and results in associative algebras (except as in 16D90), free algebras, Rings with polynomial identity, c-ideal, T-ideals, category of c-R-rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
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