Definition:Commutative and Unitary Ring
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Definition
A commutative and unitary ring $\left({R, +, \circ}\right)$ is a ring with unity which is also commutative.
That is, it is a ring such that the ring product $\left({R, \circ}\right)$ is commutative and has a identity element.
This is usually denoted by $1_R$ or $1$ and called a unity.
Alternative names
Also known as:
- Commutative and unital ring
- Commutative ring with unity
- Commutative ring with identity
Sources
- C.R.J. Clapham: Introduction to Abstract Algebra (1969)... (previous)... (next): $\S 5.18$
