Bases of Ideals With no Monomials - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T09:58:28Z http://mathoverflow.net/feeds/question/64559 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/64559/bases-of-ideals-with-no-monomials Bases of Ideals With no Monomials Santiago 2011-05-11T02:30:14Z 2011-05-11T02:30:14Z <p>Let $K$ be an algebraically closed field and $K[\underline{x}]$ its ring of polynomials in $n$ variables $x_1,\cdots, x_n$. Let $J\leq K[\underline{x}]$ be an ideal such that there are no monomials in $J$. Is there any characterization on a finite set of generators (probably a reduced Gröbner base) $G$ of $J$?</p> <p>To rephrase my question, Is there a way to know when an ideal in $K[\underline{x}]$ has no monomials by just looking at a set of finitely many generators?</p>