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I found this in a passage:

Recall that the prime subfield of a field is the smallest subfield, and is isomorphic to Fp for some p or to Q.

I noticed that every time the conjunction ( in above sentence, notice or) is used, the preposition ( in above sentence, notice to ) is also used to refer to the object.

Can it be written as:

Recall that the prime subfield of a field is the smallest subfield, and is isomorphic to Fp for some p or Q

?

  • I don't think it has to do with the word "or" or other conjunctions such as "and." Some nouns requires prepositions such as "to", "for" or "against." The word "isomorphic needs "to" because this is how it is used. It could have been another preposition. However, in any case after "or " or "and" at the end of the sentence the word isomorphic needs this preposition. – Mrt Oct 11 '18 at 23:24
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The phrase in question is is isomorphic to {something}.

It is isomorphic to {Fp, for some p} or [is isomorphic] to Q.

If we did not repeat the preposition to before "Q", it would be possible to take "Q" as an object of "for": "for some p or Q", at least grammatically.

Normally context would disambiguate. "Fp for some p or Q" can be eliminated as a possibility but not on grammatical grounds.

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To is used to tells us what else is part of relation (in the non-math sense): F is isomorphic to K.

The original parses like this

Recall that the prime subfield of a field is the smallest subfield, and is isomorphic (to Fp for some p) or (to Q).

Your version can parse like this and could be confusing intitially

✗ Recall that the prime subfield of a field is the smallest subfield, and is isomorphic to Fp for (some p or Q).

In other words, the subfield is isomorphic to Fp or FQ. You use your knowledge of the material to determine that this was not meant.

If it didn't have "for some p", then you could the omit to without confusion:

OK Recall that the prime subfield of a field is the smallest subfield, and is isomorphic to Fp or Q.

Of course, it's the author's decision on how precise they want to be with their language.

  • I've deleted my answer in favor of yours, as its better formatted and clearer. Also, who did you get the subscript notation in markdown? – sharur Oct 11 '18 at 23:46
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    <sub>p</sub> Basic features are in the Markdown Help page. However, they send you to Meta SE (here) for a complete list of allowed HTML tags. There's also the Formatting Sandbox on ELL Meta for a list of other tips. – Em. Oct 11 '18 at 23:53

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