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I'm trying to figure out all the possible right ideals of $M_{n\times n}(\mathbb{F})$.

I know that the two-sided ideals are only the trivial ones, and the proof uses the fact that we can operate on the rows and line of a matrix to make $E_{ij}$ - the matrix that has one in ij and zero in the rest of it.

Does anyone have any idea(l)?

Thanks.

user26857
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Simon Green
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  • Here are some previous posts on this question: 1, 2, 3. Do any of these answer your question? – Viktor Vaughn Dec 27 '18 at 18:35
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    Thanks for you response. I dont think so, because in my case I have the ring of matrices over a field. I think it might be related to the fact that multiplication from the right must produce a matrix with its columns spanning the ideal vector space. – Simon Green Dec 27 '18 at 19:05
  • Hm, okay. How about this one? (I realize it's about left ideals, but I think the answers can be modified for right ideals.) – Viktor Vaughn Dec 27 '18 at 19:25

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