Let $R=k[x_1,x_2,...,x_n]$ be the polynomial ring in $n$ indeterminates over a field $k$. An ideal (that can be) generated by monomials is called a monomial ideal. For the monomial ideal $M=(m_1,m_2,...,m_t)$, the radical of $M$ itself is monomial and can be written as, $Rad(M)=(\sigma(m_1),\sigma(m_2),...,\sigma(m_t))$ where $\sigma(x_1^{a_1}x_2^{a_2}...x_n^{a_n})$ is the product of indeterminates $x_i$ s.t. $a_i\geq 1$.

A binomial ideal in $R$ is generated by binomials. I was wondering if we have similar theorems for the case of binomial ideals where we can write down a generating set for the radical by just knowing a generating set of the ideal. Eisenbud and Sturmfels, in their monumental paper on binomial ideals, showed that the radical itself is binomial. I am especially interested in finding generators for radical of binomial ideals in the case where char$(k)=0$ (or even when $k=\mathbb{C}$) and what kind of binomials generate radical binomial ideals.

Becker, Grobe and Niermann discuss the case of zero dimensional binomial ideals. Ojeda and Sanchez prove some results for radicals of lattice (binomial) ideals. I have also seen some results in positive characteristic, but they are not relevant to my research.

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