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Definition of Unital: A ring $R$ is called unital, if there exists an element $u \in R$ which satisfies: $$\forall r \in R, u \cdot r = r \cdot u = r.$$
Such an element $u$ is called a multiplicative identity element in the ring $R$. When a ring $R$ possesses a multiplicative identity element, the pair $(R, \cdot)$ forms a monoid. Thus, such an element $u$ is unique, in a unital ring. For this reason, the multiplicative identity in a unital ring is often called $1$.
This definition logically relies on the following definitions and statements: Def/Group
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