On the structure of simplicial affine semigroups

2000 ◽  
Vol 130 (5) ◽  
pp. 1017-1028 ◽  
Author(s):  
J. C. Rosales ◽  
P. A. García-Sánchez
Keyword(s):  
Upper Bound ◽  
Structure Theorem ◽  
Semigroup Rings ◽  
Affine Semigroups ◽  
Affine Semigroup

We give a structure theorem for simplicial affine semigroups. From this result we deduce characterizations of some properties of semigroup rings of simplicial affine semigroups. We also compute an upper bound for the cardinality of a minimal presentation of a simplicial affine semigroup.

scholarly journals FACTORIZATION INVARIANTS IN HALF-FACTORIAL AFFINE SEMIGROUPS

2013 ◽  
Vol 23 (01) ◽  
pp. 111-122 ◽  
Author(s):  
P. A. GARCÍA SÁNCHEZ ◽  
I. OJEDA ◽  
A. SÁNCHEZ-R.-NAVARRO
Keyword(s):  
Upper Bound ◽  
Affine Semigroups ◽  
Affine Semigroup ◽  
Catenary Degree

Let [Formula: see text] be the monoid generated by [Formula: see text] We introduce the homogeneous catenary degree of [Formula: see text] as the smallest N ∈ ℕ with the following property: for each [Formula: see text] and any two factorizations u, v of a, there exist factorizations u = w1,…,wt = v of a such that, for every k, d (wk,wk+1) ≤ N, where d is the usual distance between factorizations, and the length of wk, |wk|, is less than or equal to max{|u|, |v|}. We prove that the homogeneous catenary degree of [Formula: see text] improves the monotone catenary degree as upper bound for the ordinary catenary degree, and we show that it can be effectively computed. We also prove that for half-factorial monoids, the tame degree and the ω-primality coincide, and that all possible catenary degrees of the elements of an affine semigroup of this kind occur as the catenary degree of one of its Betti elements.

Dualizing Complexes of Affine Semigroup Rings

1990 ◽  
Vol 322 (2) ◽  
pp. 561 ◽  
Author(s):  
Uwe Schafer ◽  
Peter Schenzel
Keyword(s):  
Semigroup Rings ◽  
Affine Semigroup ◽  
Dualizing Complexes

scholarly journals Divisor class groups of affine semigroup rings associated with distributive lattices

1992 ◽  
Vol 149 (2) ◽  
pp. 352-357 ◽  
Author(s):  
Mitsuyasu Hashimoto ◽  
Takayuki Hibi ◽  
Atsushi Noma
Keyword(s):  
Distributive Lattices ◽  
Semigroup Rings ◽  
Class Groups ◽  
Divisor Class ◽  
Affine Semigroup

scholarly journals On Segre products of affine semigroup rings

1988 ◽  
Vol 110 ◽  
pp. 113-128 ◽  
Author(s):  
Lê Tuân Hoa
Keyword(s):  
Positive Integer ◽  
Polynomial Ring ◽  
Semigroup Ring ◽  
Semigroup Rings ◽  
Finitely Generated ◽  
Affine Semigroup

Let N denote the set of non-negative integers. An affine semigroup is a finitely generated submonoid S of the additive monoid Nm for some positive integer m. Let k[S] denote the semigroup ring of S over a field k. Then one can identify k[S] with the subring of a polynomial ring k[t1, …, tm] generated by the monomials .

scholarly journals Measuring the non-Gorenstein locus of Hibi rings and normal affine semigroup rings

2019 ◽  
Vol 540 ◽  
pp. 78-99 ◽  
Author(s):  
Jürgen Herzog ◽  
Fatemeh Mohammadi ◽  
Janet Page
Keyword(s):  
Semigroup Rings ◽  
Affine Semigroup

scholarly journals Defining Ideals of Affine Semigroup Rings of Codimension 2

1996 ◽  
Vol 184 (3) ◽  
pp. 1161-1174 ◽  
Author(s):  
Kazufumi Eto
Keyword(s):  
Semigroup Rings ◽  
Affine Semigroup
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