Whats an example of ring $A$ which is not commutative and contains an element $x\in Z(A)$ such that the left multiplication by $x$ is an injection and $x$ is not a unit?
2026-03-25 07:42:08.1774424528
Example of a regular element in noncommutative rings
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Let $A=M_2(\Bbb Z)$ be $2\times 2$ matrices over $\Bbb Z$ and let $x=2I$ be twice the identity.