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      <h1>NCIdeal -- Type of a two-sided ideal in a noncommutative ring</h1>
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        <h2>Description</h2>
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          <p>This defines a right ideal in a noncommutative ring.</p>
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          <h2>Functions and methods returning an object of class NCIdeal:</h2>
          <ul>
            <li><span><a title="The defining ideal of an NCPolynomialRing" href="_ideal_lp__N__C__Polynomial__Ring_rp.html">ideal(NCPolynomialRing)</a> -- The defining ideal of an NCPolynomialRing</span></li>
            <li><span><a title="Defining ideal of an NCQuotientRing in its ambient ring" href="_ideal_lp__N__C__Quotient__Ring_rp.html">ideal(NCQuotientRing)</a> -- Defining ideal of an NCQuotientRing in its ambient ring</span></li>
          </ul>
          <h2>Methods that use an object of class NCIdeal:</h2>
          <ul>
            <li><span><a title="Returns a basis of an NCIdeal in a particular degree." href="_basis_lp__Z__Z_cm__N__C__Ideal_rp.html">basis(ZZ,NCIdeal)</a> -- Returns a basis of an NCIdeal in a particular degree.</span></li>
            <li><span><a title="Returns the generators of an NCIdeal" href="_generators_lp__N__C__Ideal_rp.html">generators(NCIdeal)</a> -- Returns the generators of an NCIdeal</span></li>
            <li><span><kbd>homogDual(NCIdeal)</kbd> -- see <span><a title="Computes the dual of a pure homogeneous ideal" href="_homog__Dual.html">homogDual</a> -- Computes the dual of a pure homogeneous ideal</span></span></li>
            <li><span><a title="Determines whether the input defines a homogeneous object" href="_is__Homogeneous_lp__N__C__Ideal_rp.html">isHomogeneous(NCIdeal)</a> -- Determines whether the input defines a homogeneous object</span></li>
            <li><span><kbd>ncGroebnerBasis(NCIdeal)</kbd> -- see <span><a title="Compute a noncommutative Groebner basis." href="_nc__Groebner__Basis.html">ncGroebnerBasis</a> -- Compute a noncommutative Groebner basis.</span></span></li>
            <li><span><a title="Sum of NCIdeals" href="___N__C__Ideal_sp_pl_sp__N__C__Ideal.html">NCIdeal + NCIdeal</a> -- Sum of NCIdeals</span></li>
            <li><span><a title="Construct a NCQuotientRing" href="___N__C__Polynomial__Ring_sp_sl_sp__N__C__Ideal.html">NCPolynomialRing / NCIdeal</a> -- Construct a NCQuotientRing</span></li>
            <li><span><a title="Apply a ring map to the generators of an ideal" href="___N__C__Ring__Map_sp__N__C__Ideal.html">NCRingMap NCIdeal</a> -- Apply a ring map to the generators of an ideal</span></li>
            <li><span><kbd>quadraticClosure(NCIdeal)</kbd> -- see <span><a title="Creates the subideal generated by quadratic elements of a given ideal" href="_quadratic__Closure.html">quadraticClosure</a> -- Creates the subideal generated by quadratic elements of a given ideal</span></span></li>
            <li><span><a title="Returns the ring of an NCIdeal or NCGroebnerBasis" href="_ring_lp__N__C__Ideal_rp.html">ring(NCIdeal)</a> -- Returns the ring of an NCIdeal or NCGroebnerBasis</span></li>
            <li><span><kbd>twoSidedNCGroebnerBasisBergman(NCIdeal)</kbd> -- see <span><a title="Calls Bergman to compute a two sided noncommutative Groebner Basis." href="_two__Sided__N__C__Groebner__Basis__Bergman.html">twoSidedNCGroebnerBasisBergman</a> -- Calls Bergman to compute a two sided noncommutative Groebner Basis.</span></span></li>
          </ul>
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          <h2>For the programmer</h2>
          <p>The object <a title="Type of a two-sided ideal in a noncommutative ring" href="___N__C__Ideal.html">NCIdeal</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</a> &lt; <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">Thing</a>.</p>
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          <p>The source of this document is in <span class="tt">NCAlgebra/NCAlgebraDoc.m2:1952:0</span>.</p>
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