CommutativeRings

$$\operatorname{CommutativeRings}$$

This abstract set has as elements all sets satisfying the ring axioms with commutative multiplication.

$$\mathbb{Z} \in \operatorname{CommutativeRings}$$

An example of a commutative ring.

$$\operatorname{M}_{2 \times 2}\!\left(\mathbb{Z}\right) \notin \operatorname{CommutativeRings}$$

An example of a noncommutative ring.

$$\left(R \in \operatorname{CommutativeRings} \;\mathbin{\operatorname{and}}\; x, y \in R\right) \implies \left({\left(x + y\right)}^{2} = {x}^{2} + 2 x y + {y}^{2}\right)$$

An identity valid in commutative rings.

Last updated: 2020-03-06 00:22:16