When I strongly believe in an idea, theory, ideology etc
Which one is right : I am embeded in that idea / That idea is embeded in me
or Is there another sentence, which is more appropriate, being able to substitue?
(always welcome your advice on my writing not only about the main question)
To say an idea is embedded in you seems reasonable - I would take it to mean that the idea is fully understood, has become part of your thinking, and isn't likely to be forgotten until it is fully realised.
To say that you are embedded in the idea sounds odd - how could you be within an idea? The idea might involve you, but there isn't really a process of putting you within an idea that could be described as 'embedding'. It would of course depend on the context you had created around it.
If you are trying to say that you are fully committed to the idea and its realisation, the idiomatic expression would be "I am invested in that idea".
The past tense is embedded, but Oxford defines embed as
implant (an idea or feeling) so that it becomes ingrained within a particular context.
"the Victorian values embedded in Tennyson's poetry"
It sounds odd to me to speak of ideas being embedded in a person. You could say you were wedded to the idea, or that it had been instilled in you.
You might say that the idea is ingrained in you.
According to Cambridge Dictionary:
(of beliefs) so firmly held that they are not likely to change:
"Such ingrained prejudices cannot be corrected easily."
"The belief that you should own your house is deeply ingrained in our society."
