Definition:Unity
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Definition
Let $\left({R, +, \circ}\right)$ be a ring.
If the semigroup $\left({R, \circ}\right)$ has an identity, this identity is referred to as the unity of the ring $\left({R, +, \circ}\right)$.
It is (usually) denoted $1_R$, where the subscript denotes the particular ring to which $1_R$ belongs (or often $1$ if there is no danger of ambiguity).
The ring itself is then referred to as a ring with unity.
Sources
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 55 \ (2)$
