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what does this notation mean:

$(\chi(D),p^j)$

where $\chi(D)$ - character of the group ring. D - element of the group of ring, p - prime number.

It is looks like a greatest common divisor, but it is not.

I found this notation in the book Addition theorems, H. B. MANN, 1965. https://www.amazon.com/Addition-Theorems-H-B-Mann/dp/047056735X without explanation: enter image description here

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  • $\begingroup$ Why do you think it is not the GCD? That would work in the proof, no? $\endgroup$ Sep 15 at 11:11
  • $\begingroup$ Yes it is GCD!!! Thank you! $\endgroup$ Sep 15 at 12:06

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I am sorry, but the comment of David A. Craven help me to understand that it is in fact the greatest common divisor but in algebraic number field.

In fact, if we accept that this is a GCD, then the proof of the theorem will be true, as can be seen in the attached screenshot.

The prime number decomposition in algebraic number field confused me a little, so I did not immediately understand this notation.

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    $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Sep 15 at 12:24

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