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Un módulo es una estructura algebraica un poco más sencilla que la de anillo. Para su definición utilizaremos un poco de las nociones de teoría de grupo y anillos, por consecuente, hay que tener una noción un de los conceptos que allí se presentan. Ahora definimos lo que es un módulo;
Definición 1: (módulo)
Sea (A, +, ·) un anillo unitario. Un A-módulo izquierdo es una terna (M, +, ·) tal que M es un conjunto con dos relaciones binarias definidas (una interna y otra externa (con un dominio de operadores en A)), es decir,
+: M x M → M ·: A x M → A
Además se han de cumplir las siguientes condiciones:
- (M, +, ·) es un grupo conmutativo.
- a(r + s) = ar + as; para todo a pertenece a A y r,s en M.
- (a + b)r = ar + br; para todo a, b pertenece a A y r en M.
- (ab)r= a(br), idem.
- 1r=r, para todo r en M.
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