Lifting Problem in Codimension 2 and Initial Ideals

lifting problem in codimension 2 and initial ideals

Syzygies of Codimension 2 Lattice Ideals

The study of semigroup algebras has a long tradition in commutative algebra. Presentation ideals of semigroup algebras are called toric ideals, in reference to their prominent role in geometry. In this paper we consider the more general class of lattice ideals. Fix a polynomial ring S = k[x1, . . . , xn] over a field k and identify monomials x in S with vectors a ∈ N. Let L be any sublattice of...

APPROXIMATE IDENTITY IN CLOSED CODIMENSION ONE IDEALS OF SEMIGROUP ALGEBRAS

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.

Lifting Chains of Prime Ideals

We give an elementary proof that for a ring homomorphism A → B satisfying the property that every ideal in A is contracted from B the following property holds: for every chain of prime ideals p0 ⊂ . . . ⊂ pr in A there exists a chain of prime ideals q0 ⊂ . . . ⊂ qr in B such that qi ∩ A = pi. Mathematical Subject Classification (1991): 13B24. Let A and B be commutative rings and let φ : A → B b...

Single Spot Ideals of Codimension 3 and Long Bourbaki Sequences

Abstract. Let K be a field and S = K[x1, . . . , xn] be a polynomial ring. A single spot ideal I ⊂ S is a graded ideal whose local cohomology H m (S/I), i < dimS/I and m = (x1, . . . , xn), only has non-trivial value N , a finite length module, at i = depthS/I. We consider characterization of single spot ideals in terms of (long) Bourbaki sequences. The codimension 2 case has been fairly well i...

Initial Ideals of Truncated Homogeneous Ideals

Denote by R the power series ring in countably many variables over a eld K; then R 0 is the smallest sub-algebra of R that contains all homogeneous elements. It is a fact that a homogeneous, nitely generated ideal J in R 0 have an initial ideal gr(J), with respect to an arbitrary admissible order, that is locally nitely generated in the sense that dimK gr(J) d P d?1 j=1 R 0 j gr(J) d?j < 1 for ...