fix: proofread Algebraic NT I: Rings of Integers part

[vEnhance]

Proofreading pass over the Algebraic NT I: Rings of Integers part (part of the proofreading campaign, #315). Covers tex/alg-NT/numfield.tex, norm-trace.tex, dedekind.tex, classgrp.tex, discriminant.tex, pell.tex.

All findings were minor: typos, grammar, and a notation slip. No large mathematical errors were found — the arguments and computations checked out.

Fixes

norm-trace.tex

• "the conjugates of $\alpha$ does not lie" → "do not lie" (subject-verb agreement).
• "and we misses $\beta$" / "we misses $\alpha$" → "we miss …" (2×).

dedekind.tex

• In the factoring-algorithm solution: "$\OO_K/(\kp_i)$ has degree $p^{\deg f_i}$" → "$\OO_K/\kp_i$ has size $p^{\deg f_i}$" (matches the parallel sentence above it; also dropped the stray parentheses around the prime ideal).

classgrp.tex

• "overlap one onto the another" → "onto the other".
• Stray artifact: "implying the result $id(\kb) \mid (n)$" → "$\kb \mid (n)$".
• The trace matrix $[\Tr(\alpha_i\alpha_j)]$ has determinant $d$ (the discriminant), which is generally not $\pm 1$, so it is not in $\GL_n(\ZZ)$. Changed "$\in \GL_n(\ZZ)$ with determinant $d$" → "$\in \Mat_n(\ZZ)$ with determinant $d$".
• $\Delta_K = 20$ → $\Delta_K = -20$ for $\QQ(\sqrt{-5})$ (in the Korea 2014 solution, 2×), consistent with the sign convention used elsewhere in the chapter (e.g. $\Delta_K = -67$, $-68$, $-4$).

pell.tex

• Battle-of-Hastings quote transcription typos: "war-hatched" → "war-hatchet", and "one might square of men" → "one mighty square of men".

Closes the Algebraic NT I: Rings of Integers checkbox in #315.

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