# Answer to Question #17269 in Algebra for sanches

Question #17269

Show that if I in R is a modular left ideal, then I can be embedded in a modular maximal left ideal of R

Expert's answer

Fix the element

*e*above. Forany left ideal*I'**⊇**I*, we have*I'*is not equal*R*iff*e*is not in*I'*. (For the “only if”part, note that if*e**∈**I'*, then,for any*r**∈**R*, we have*r**∈**re*+*I**⊆**I'*.) Therefore, we can apply Zorn’s Lemma to thefamily of left ideals*{I'*:*I*is not equal*R*and*I_**⊇**I}*to prove the existence of a maximal left idealm containing*I*. Clearly, m is also modular, and*e*is not in*m.*Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment