field '''''r'' algebra''' ''r'' module associative ''r'' bilinear binary operation also contains multiplicative identity examples concept ''s'' ring center ''c'' ''s'' associative ''c'' algebra definition let ''r'' commutative ring ''r'' could field '''associative ''r'' algebra''' simply '''''r'' algebra''' ring also ''r'' module way two additions ring addition module addition operation scalar multiplication satisfies math r cdot xy r cdot x x r cdot math
Formal science Mathematics Pure mathematics Algebra Associative algebra