scholarly journals Binomial generation of the radical of a lattice ideal

2010 ◽  
Vol 324 (6) ◽  
pp. 1334-1346 ◽  
Author(s):  
Anargyros Katsabekis ◽  
Marcel Morales ◽  
Apostolos Thoma
Keyword(s):  
Lattice Ideal

scholarly journals Computing the degree of a lattice ideal of dimension one

2014 ◽  
Vol 65 ◽  
pp. 15-28 ◽  
Author(s):  
Hiram H. López ◽  
Rafael H. Villarreal
Keyword(s):  
Lattice Ideal ◽  
Dimension One

scholarly journals The short resolution of a lattice ideal

2002 ◽  
Vol 131 (4) ◽  
pp. 1081-1091 ◽  
Author(s):  
Pilar Pisón Casares
Keyword(s):  
Lattice Ideal

scholarly journals COMPLETE INTERSECTIONS IN BINOMIAL AND LATTICE IDEALS

2013 ◽  
Vol 23 (06) ◽  
pp. 1419-1429 ◽  
Author(s):  
HIRAM H. LÓPEZ ◽  
RAFAEL H. VILLARREAL
Keyword(s):  
Complete Intersection ◽  
Characteristic Zero ◽  
Positive Characteristic ◽  
Complete Intersections ◽  
Lattice Ideals ◽  
The Family ◽  
Lattice Ideal ◽  
Arbitrary Lattice ◽  
Intersection Criterion ◽  
Graded Lattice

For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set-theoretic complete intersections. In characteristic zero, we show that an arbitrary lattice ideal which is a binomial set-theoretic complete intersection is a complete intersection.

scholarly journals THE SHORT RESOLUTION OF A SEMIGROUP ALGEBRA

2017 ◽  
Vol 96 (3) ◽  
pp. 400-411 ◽  
Author(s):  
I. OJEDA ◽  
A. VIGNERON-TENORIO
Keyword(s):  
Semigroup Algebra ◽  
Numerical Semigroups ◽  
Frobenius Numbers ◽  
Affine Semigroups ◽  
Affine Semigroup ◽  
Lattice Ideal ◽  
Apéry Sets

This work generalises the short resolution given by Pisón Casares [‘The short resolution of a lattice ideal’, Proc. Amer. Math. Soc.131(4) (2003), 1081–1091] to any affine semigroup. We give a characterisation of Apéry sets which provides a simple way to compute Apéry sets of affine semigroups and Frobenius numbers of numerical semigroups. We also exhibit a new characterisation of the Cohen–Macaulay property for simplicial affine semigroups.

scholarly journals A Note on Commutative l-Groups

1971 ◽  
Vol 12 (1) ◽  
pp. 69-74 ◽  
Author(s):  
T. P. Speed ◽  
E. Strzelecki
Keyword(s):  
Vector Lattice ◽  
Sufficient Conditions ◽  
Lattice Ordered Group ◽  
Ordered Group ◽  
Vector Lattices ◽  
Complete Vector Lattice ◽  
Lattice Ideal ◽  
Complete Vector ◽  
Necessary And Sufficient ◽  
Wide Family

Let G be a commutative lattice ordered group. Theorem 1 gives necessary and sufficient conditions under which a⊥ with a∈G is a maximal l-ideal. A wide family of, l-groups G having the property that the orthogonal complement of each atom is a maximal l-ideal is described. Conditionally σ-complete and hence conditionally complete vector lattices belong to the family.It follows immediately that if a is an atom in a conditionally complete vector lattice then a⊥ is a maximal vector lattice ideal. This theorem has been proved in [7] by Yamamuro. Theorem 2 generalizes another result contained in [7]. Namely we prove that if M is a closed maximal l-ideal of an archimedean l-group G then there exists an atom a ∈ G such that M = a⊥.

The linear transformation that relates the canonical and coefficient embeddings of ideals in cyclotomic integer rings

2017 ◽  
Vol 13 (09) ◽  
pp. 2277-2297
Author(s):  
Scott C. Batson
Keyword(s):  
Linear Transformation ◽  
Algebraic Integer ◽  
The Core ◽  
Ideal Lattices ◽  
Shortest Vector Problem ◽  
The Matrix ◽  
Recent Developments ◽  
Integer Ring ◽  
Lattice Ideal ◽  
Lattice Based Cryptography

The geometric embedding of an ideal in the algebraic integer ring of some number field is called an ideal lattice. Ideal lattices and the shortest vector problem (SVP) are at the core of many recent developments in lattice-based cryptography. We utilize the matrix of the linear transformation that relates two commonly used geometric embeddings to provide novel results concerning the equivalence of the SVP in these ideal lattices arising from rings of cyclotomic integers.

scholarly journals Discrete structure spaces of ƒ-rings

1974 ◽  
Vol 18 (1) ◽  
pp. 104-110 ◽  
Author(s):  
Peter D. Colville
Keyword(s):  
Subdirect Product ◽  
Prime Ideals ◽  
Discrete Structure ◽  
Lattice Ideal ◽  
F Ring ◽  
Algebraic Ideal

Birkhoff and Pierce [2] introduced the concept of an ƒ-ring and showed that an l-ring is an f-ring if and only if it is a subdirect product of totallyordered rings. An l-ideal of an f-ring R is an algebraic ideal which is at the same time a lattice ideal of R. Structure spaces (i.e. sets of prime ideals endowed with the so-called hull-kernel or Stone topology) for ordinary rings have been studied by many authors. In this paper we consider certain analogues for ƒ-rings, and give characterisations of ƒ-rings for which these structure spaces are discrete.

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