Noncommutative unique factorization domain

<h2 id="examples">Examples</h2>
<ul><li>The <a href="/facts/Ring_(mathematics)/JnCUXz63">ring</a> of <a href="/facts/Hurwitz_quaternion/IJ0hdSgN">Hurwitz quaternions</a>, also known as integral <a href="/facts/Quaternion/T3tnu7mX">quaternions</a>. A quaternion <i>a</i> = <i>a</i>0 + <i>a</i>1i + <i>a</i>2j + <i>a</i>3k is integral if either all the coefficients <i>a</i>i are <a href="/facts/Integer/PUwwrawx">integers</a> or all of them are <a href="/facts/Half-integer/oJ29mf8G">half-integers</a>.</li></ul>
<ul><li>All <a href="/facts/Free_algebra/xMrT0WbT">free associative algebras</a>.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a></li></ul>

<ul><li>P.M. Cohn, "Noncommutative unique factorization domains", <i>Transactions of the American Mathematical Society</i> 109:2:313-331 (1963). <a href="https://www.ams.org/journals/tran/1963-109-02/S0002-9947-1963-0155851-X/S0002-9947-1963-0155851-X.pdf">full text</a></li>
<li>R. Sivaramakrishnan, <i>Certain number-theoretic episodes in algebra</i>, CRC Press, 2006, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-8247-5895-1</li></ul>
<h2 id="notes">Notes</h2>

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

Noncommutative unique factorization domain open-in-new

Noncommutative unique factorization domain