12D10 Polynomials: location of zeros (algebraic theorems) {For the analytic theory, see <a href="#code:26C10">26C10</a>, <a href="#code:30C15">30C15</a>}

12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also <a href="#code:11Exx">11Exx</a>]

12D99 None of the above, but in this section

12E15 Skew fields, division rings [See also <a href="#code:11R52">11R52</a>, <a href="#code:11R54">11R54</a>, <a href="#code:11S45">11S45</a>, <a href="#code:16Kxx">16Kxx</a>]

12E20 Finite fields (field-theoretic aspects)

12E25 Hilbertian fields; Hilbert's irreducibility theorem

12E99 None of the above, but in this section

12F10 Separable extensions, Galois theory

12F99 None of the above, but in this section

12Gxx Homological methods (field theory)

12G05 Galois cohomology [See also <a href="#code:14F22">14F22</a>, <a href="#code:16Hxx">16Hxx</a>, <a href="#code:16K50">16K50</a>]

12G99 None of the above, but in this section

12Hxx Differential and difference algebra

12H05 Differential algebra [See also <a href="#code:13Nxx">13Nxx</a>]

12H10 Difference algebra [See also <a href="#code:39Axx">39Axx</a>]

12H20 Abstract differential equations [See also <a href="#code:34Mxx">34Mxx</a>]

12H25 $p$-adic differential equations [See also <a href="#code:11S80">11S80</a>, <a href="#code:14G20">14G20</a>]

12H99 None of the above, but in this section

12J20 General valuation theory [See also <a href="#code:13A18">13A18</a>]

12J25 Non-Archimedean valued fields [See also <a href="#code:30G06">30G06</a>, <a href="#code:32P05">32P05</a>, <a href="#code:46S10">46S10</a>, <a href="#code:47S10">47S10</a>]

12J27 Krasner-Tate algebras [See mainly <a href="#code:32P05">32P05</a>; see also <a href="#code:46S10">46S10</a>, <a href="#code:47S10">47S10</a>]

12J99 None of the above, but in this section

12K05 Near-fields [See also <a href="#code:16Y30">16Y30</a>]

12K10 Semifields [See also <a href="#code:16Y60">16Y60</a>]

12K99 None of the above, but in this section

12L05 Decidability [See also <a href="#code:03B25">03B25</a>]