Rings. Additional structure.

As structure is added to rings, a number of useful concepts are graced with definitions.

• [What?]: a ring whose multiplicative operation is commutative.
• [What?]: a ring where all nonzero elements have two-sided multiplicative inverses.
• [What?]: a ring whose multiplicative operation is commutative and no nonzero element is a zero divisor.
• [What?]: satisfies both 1) and 2) above.

The zero ring is specifically excluded from being considered to be either [...] or [...], despite otherwise meeting the requirements.