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some $$ added
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edit approved Oct 24, 2017 at 15:01
user 1
edit approved Oct 24, 2017 at 15:01
user 1
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Since it is a complementary subspace it has codimension one in L$L$, and so is maximal. It is an ideal of L$L$ because L^2$L^2$ is inside M$M$.

Since it is a complementary subspace it has codimension one in L, and so is maximal. It is an ideal of L because L^2 is inside M.

Since it is a complementary subspace it has codimension one in $L$, and so is maximal. It is an ideal of $L$ because $L^2$ is inside $M$.

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David Towers
David Towers
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Since it is a complementary subspace it has codimension one in L, and so is maximal. It is an ideal of L because L^2 is inside M.