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In EGA IV, Lemma 6.4.1.16.14.1.1, the first sentence is

Soit $R$ un anneau composé direct d'un nombre fini de corps.

I'm guessing this means

Let $R$ be a ring that is the direct product of a finite number of fields,

but I'm not positive. For one thing, "produit direct" seems to be the more usual term for "direct product." I've tried looking up "composé direct" on Google and on Wikipedia.fr, and I have not been able to find a definitive reference. I'm also confused by the fact that "direct" appears to be an adjective in the French, but I can't see what noun it might be modifying if my translation is correct. Google translate gives

Let R be a ring composed of a direct finite number of bodies.

Obviously, "bodies" should be "fields," but it still does not seem to be helpful. Thus, my question:

Question: What does "composé direct" mean in this context? In particular, why is "direct" being used as an adjective?

Secondary Question: Is there a good reason that "composé direct" is being used here rather than another, more searchable term such as "produit direct"?

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# What does "composé direct" mean in mathematical French?

In EGA IV, Lemma 6.4.1.1, the first sentence is

Soit $R$ un anneau composé direct d'un nombre fini de corps.

I'm guessing this means

Let $R$ be a ring that is the direct product of a finite number of fields,

but I'm not positive. For one thing, "produit direct" seems to be the more usual term for "direct product." I've tried looking up "composé direct" on Google and on Wikipedia.fr, and I have not been able to find a definitive reference. I'm also confused by the fact that "direct" appears to be an adjective in the French, but I can't see what noun it might be modifying if my translation is correct. Google translate gives

Let R be a ring composed of a direct finite number of bodies.

Obviously, "bodies" should be "fields," but it still does not seem to be helpful. Thus, my question:

Question: What does "composé direct" mean in this context? In particular, why is "direct" being used as an adjective?

Secondary Question: Is there a good reason that "composé direct" is being used here rather than another, more searchable term such as "produit direct"?