let s be a locally compact topological foundation semigroup with identity and ma(s) be its semigroup algebra. in this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $m_a(s)$ of a locally compact topological foundationsemigroup with identity.

A main ingredient for Kustin–Miller unprojection, as developed in [PR], is the module HomR(I, ωR), where R is a local Gorenstein ring and I a codimension one ideal with R/I Gorenstein. We prove a method of calculating it in a relative setting using resolutions. We give three applications. In the first we generalise a result of [CFHR]. The second and the third are about Tom and Jerry, two famili...

Let X be a nonsingular algebraic variety. Suppose Z ⊆ X is a closed subscheme of X, with ideal sheaf IZ . When Z has codimension one in X, everything is as nice as it could be: IZ is a locally free sheaf, in fact a line bundle, and Z can locally be defined by a single equation. But starting in codimension two, all these pleasant things are usually false. To begin with, not every closed subschem...

Generic linkage is used to compute a prime ideal such that the radical of the initial ideal of the prime ideal is equal to the radical of a given codimension two monomial ideal that has a Cohen-Macaulay quotient ring.

The inverse Gröbner basis problem is to find the ideals that have a given monomial ideal as its initial ideal. We consider the problem of finding when the given monomial ideal is the initial ideal of a prime ideal. Kalkbrenner and Sturmfels (1995), in Theorem 1, prove that the radical of the initial ideal of a prime ideal is equi-dimensional and connected in codimension one or equivalently, the...