7:15 AM
Two new tags: and . Both of them created by Intuition.
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How can I prove that the ring of all $2*2$ matrices $$\begin{equation*} \begin{bmatrix} a & b \\ 0 & c \end{bmatrix} \qquad \end{equation*}$$ Such that $a$ is an integer and $b,c$ are rationals is right Noetherian but not left Noetherian. I have seen a lot of discussions here about it but I sti...

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Prove that the Jacobson radical of a ring $R$ contains no idempotents other than $0$.could anyone give me a hint please?