Approximation property (ring theory)

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Artin_approximation_theorem/gKTgeGnR">Artin approximation theorem</a></li>
<li><a href="/facts/Popescu%2527s_theorem/pnVY4nDS">Popescu's theorem</a></li></ul>
<h2 id="notes">Notes</h2>

<ul><li>Popescu, Dorin (1986). <a href="https://projecteuclid.org/download/pdf_1/euclid.nmj/1118780554">"General Néron desingularization and approximation"</a>. <i>Nagoya Mathematical Journal</i>. 104: 85–115. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1017%2FS0027763000022698">10.1017/S0027763000022698</a>.</li>
<li><a href="/facts/Christel_Rotthaus/j9ujHVTD">Rotthaus, Christel</a> (1987). "On the approximation property of excellent rings". <i><a href="/facts/Inventiones_Mathematicae/bARcL95Y">Inventiones Mathematicae</a></i>. 88: 39–63. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1987InMat..88...39R">1987InMat..88...39R</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF01405090">10.1007/BF01405090</a>.</li>
<li>Artin, M (1969). <a href="http://www.numdam.org/item/PMIHES_1969__36__23_0/">"Algebraic approximation of structures over complete local rings"</a>. <i>Publications Mathématiques de l'IHÉS</i>. 36: 23–58. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF02684596">10.1007/BF02684596</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0073-8301">0073-8301</a>.</li>
<li>Artin, M (1968). "On the solutions of analytic equations". <i>Inventiones Mathematicae</i>. 5 (4): 277–291. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/1968InMat...5..277A">1968InMat...5..277A</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF01389777">10.1007/BF01389777</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0020-9910">0020-9910</a>.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Rotthaus, Christel (1997). "Excellent Rings, Henselian Rings, and the Approximation Property". Rocky Mountain Journal of Mathematics. 27 (1): 317–334. doi:10.1216/rmjm/1181071964. JSTOR 44238106. <a href="https://doi.org/10.1216%2Frmjm%2F1181071964" target="_blank">https://doi.org/10.1216%2Frmjm%2F1181071964</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>"Tag 07BW: Smoothing Ring Maps". The Stacks Project. Columbia University, Department of Mathematics. Retrieved 2018-02-19. <a href="https://stacks.math.columbia.edu/tag/07BW" target="_blank">https://stacks.math.columbia.edu/tag/07BW</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
</ol>

Approximation property (ring theory) open-in-new

Approximation property (ring theory)