We calculate the real rank and stable rank of CCR algebras which either have only finite dimensional irreducible representations or have finite topological dimension. We show that either rank of A is determined in a good way by the ranks of an ideal I and the quotient A/I in four cases: When A is CCR; when I has only finite dimensional irreducible representations; when I is separable, of genera...

In this paper, we introduce a modified Van der Waerden algorithm to decompose a variety into the union of irreducible varieties. We give an effective representation for irreducible varieties obtained by the algorithm, which allows us to obtain an irredundant decomposition easily. We show that in the zero dimensional case, the polynomial systems for the irreducible varieties obtained in the Van ...

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...

We give the definition of D-invariant points on an irreducible algebraic hypersurface V in RN. show that every regular point quadratic RN is D-invariant. prove local Taylor interpolation projector at a 2 ideal if and only

We compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface (T, `) corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques to extend the ideas of Arcara and Bertram to express wall-crossings as Mukai flops and show that the moduli spaces are projective.

We prove the GSS conjecture of Garcia, Stillman and Sturmfels, which states that the ideal of the variety of secant lines to a Segre product of projective spaces is generated by 3 × 3 minors of flattenings. We also describe the decomposition of the coordinate ring of this variety as a sum of irreducible representations.

We pose a conjecture for the expected number of generators of the ideal of the union C of s general rational irreducible curves in P r. By using the computer we prove the conjecture for C of low degree d (e.g. if s = 1 for d 80 and if s 10 for d 40).

Given a right ideal I in ring R, the idealizer of R is largest subring which becomes two-sided ideal. In this paper we consider idealizers second Weyl algebra A2, differential operators on k[x,y] (in characteristic 0). Specifically, let f be polynomial x and y defines an irreducible curve whose singularities are all cusps. We show that fA2 A2 always left noetherian, extending work McCaffrey.

We investigate Sharifan and Moradi’s closed neighborhood ideal of a finite simple graph, which is square-free monomial in polynomial ring over field. explicitly describe the minimal irreducible decompositions these ideals. also characterize trees whose ideals are Cohen–Macaulay; particular, this property for characteristic independent.

We investigate the symmetry component of the center variety of polynomial differential systems, corresponding to systems with an axis of symmetry in the real plane. We give a general algorithm to find this component, compute its dimension and show that it is irreducible. We show that our methods provide a simple way to compute the radical of the ideal generated by the focus quantities and, ther...