Part of the Graduate Texts in Mathematics book series (GTM, volume 211)
A ring A is a set, together with two laws of composition called multiplication and addition respectively, and written as a product and as a sum respectively, satisfying the following conditions:
- RI 1.
With respect to addition, A is a commutative group.
- RI 2.
The multiplication is associative, and has a unit element.
- RI 3.For all x, y, z ∈ A we have$$ (x + y)z = xz + yz and z(x + y) = zx + zy. $$
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