Cohen–Macaulay quotients of normal semigroup rings via irreducible resolutions

Cohen–macaulay Quotients of Normal Semigroup Rings via Irreducible Resolutions

For a radical monomial ideal I in a normal semigroup ring k[Q], there is a unique minimal irreducible resolution 0 → k[Q]/I → W 0 → W 1 → · · · by modules W i of the form ⊕ j k[Fij ], where the Fij are (not necessarily distinct) faces of Q. That is, W i is a direct sum of quotients of k[Q] by prime ideals. This paper characterizes Cohen–Macaulay quotients k[Q]/I as those whose minimal irreducib...

Divisorial Linear Algebra of Normal Semigroup Rings

We investigate the minimal number of generators μ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the semigroup. The main result is that for every bound C there exist, up to isomorphism, only finitely divisorial ideals I such that μ(I) ≤ C. It follows that there...

new semigroup compactifications via the enveloping semigroups of associated flows

this thesis deals with the construction of some function algebras whose corresponding semigroup compactification are universal with respect to some properies of their enveloping semigroups. the special properties are of beigan a left zero, a left simple, a group, an inflation of the right zero, and an inflation of the rectangular band.

Quotients of Representation Rings

We give a proof using so-called fusion rings and q-deformations of Brauer algebras that the representation ring of an orthogonal or symplectic group can be obtained as a quotient of a ring Gr(O(∞)). This is obtained here as a limiting case for analogous quotient maps for fusion categories, with the level going to ∞. This in turn allows a detailed description of the quotient map in terms of a re...

Rings of Quotients of Rings of Functions