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

In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.

The first author had shown earlier that for a standard graded ring R and ideal I in characteristic p > 0 , with ? ( / ) < ? there exists compactly supported continuous function f whose Riemann integral is the HK multiplicity e H K . We explore further some other invariants, namely shape of graph m (where maximal maximum support (denoted as ? In case domain dimension d ? 2 we prove regular if on...

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.

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we will introduce the notions of 2-absorbing $I$-prime and 2-absorbing $I$-second submodules of an $R$-module $M$ as a generalization of 2-absorbing and strongly 2-absorbing second submodules of $M$ and explore some basic properties of these classes of modules.

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 derive group theoretical methods to test if a lattice is strongly modular. We then apply these methods to the lattices of rational irreducible maximal nite groups.

We give another proof of a theorem of Scharlemann and Tomova and of a theorem of Hartshorn. The two theorems together say the following. Let M be a compact orientable irreducible 3–manifold and P a Heegaard surface of M . Suppose Q is either an incompressible surface or a strongly irreducible Heegaard surface in M . Then either P ∩ Q = ∅ after an isotopy or the Hempel distance d(P ) ≤ 2genus(Q)...

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).