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Partial algebra
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<h2 id="examples">Example(s)</h2> <ul><li><a href="/facts/Partial_groupoid/0dtM29cJ">partial groupoid</a></li> <li><a href="/facts/Field_(mathematics)/xAjAS4ko">field</a> — the multiplicative inversion is the only proper partial operation<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a></li> <li><a href="/facts/Effect_algebra/lf3JEbCb">effect algebras</a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a></li></ul> <h2 id="structure">Structure</h2> <p>There is a "Meta Birkhoff Theorem" by Andreka, Nemeti and Sain (1982).<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> </p> <h2 id="further-reading">Further reading</h2> <ul><li>Peter Burmeister (2002) [1986]. <i>A Model Theoretic Oriented Approach to Partial Algebras</i>. <a href="/facts/CiteSeerX_(identifier)/SceDmd3c">CiteSeerX</a> <a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.6134">10.1.1.92.6134</a>.</li> <li>Horst Reichel (1984). <i>Structural induction on partial algebras</i>. Akademie-Verlag.</li> <li>Horst Reichel (1987). <i>Initial computability, algebraic specifications, and partial algebras</i>. Clarendon Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-19-853806-6.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Peter Burmeister (1993). "Partial algebras—an introductory survey". In Ivo G. Rosenberg; Gert Sabidussi (eds.). Algebras and Orders. Springer Science & Business Media. pp. 1–70. ISBN 978-0-7923-2143-9. <a href="978-0-7923-2143-9" target="_blank">978-0-7923-2143-9</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>George A. Grätzer (2008). Universal Algebra (2nd ed.). Springer Science & Business Media. Chapter 2. Partial algebras. ISBN 978-0-387-77487-9. <a href="978-0-387-77487-9" target="_blank">978-0-387-77487-9</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Peter Burmeister (1993). "Partial algebras—an introductory survey". In Ivo G. Rosenberg; Gert Sabidussi (eds.). Algebras and Orders. Springer Science & Business Media. pp. 1–70. ISBN 978-0-7923-2143-9. <a href="978-0-7923-2143-9" target="_blank">978-0-7923-2143-9</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Foulis, D. J.; Bennett, M. K. (1994). "Effect algebras and unsharp quantum logics". Foundations of Physics. 24 (10): 1331. Bibcode:1994FoPh...24.1331F. doi:10.1007/BF02283036. hdl:10338.dmlcz/142815. S2CID 123349992. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Peter Burmeister (1993). "Partial algebras—an introductory survey". In Ivo G. Rosenberg; Gert Sabidussi (eds.). Algebras and Orders. Springer Science & Business Media. pp. 1–70. ISBN 978-0-7923-2143-9. <a href="978-0-7923-2143-9" target="_blank">978-0-7923-2143-9</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> </ol>