0x = 0 = x0

Dependencies:

1. Ring

Let $R$ be a ring. Then $\forall x \in R, 0{\cdot}x = 0 = x{\cdot}0$.

Proof

$0x = (0+0)x = 0x + 0x$. Therefore, $0x = 0$.

$x0 = x(0+0) = x0 + x0$. Therefore, $x0 = 0$.

Dependency for:

1. (-a)b = a(-b) = -ab
2. A field is an integral domain

Info:

• Depth: 2
• Number of transitive dependencies: 2

Transitive dependencies:

1. Group
2. Ring