Definition:Unit of Algebra
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Definition
Let $R$ be a commutative ring.
Let $\struct {A_R, \oplus}$ be a unital algebra over $R$.
The unit of $\struct {A_R, \oplus}$, denoted $1_A$, is the identity element of the operation $\oplus$:
- $\forall a \in A_R: a \oplus 1_A = 1_A \oplus a = a$
It is usually denoted $1$ when there is no source of confusion with the identity elements of the underlying structures of the algebra.
Also known as
The unit of a unital algebra can also be referred to as its multiplicative identity.
Also see