''a'' automatically ''r'' module since ''r'' nbsp nbsp ''x'' ''r'' sub ''a'' sub ''x'' gives quotient ring ''a'' nbsp nbsp ''i'' structure ''r'' module fact ''r'' algebra follows ring homomorphic image ''a'' also ''r'' algebra direct products direct product family ''r'' algebras ring theoretic direct product becomes ''r'' algebra obvious scalar multiplication free products one form free product ''r'' algebras manner similar free product groups free product coproduct category ''r'' algebras tensor products tensor product two
Formal science Mathematics Pure mathematics Algebra Associative algebra