The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

This book is an extended and revised version of" Numerical Semigroups with Applications,"
published by Springer as part of the RSME series. Like the first edition, it presents …

Theorem l we show that ifk has positive characteristic, and a, b, care pairwise coprime, then
0 P (a, b, c)(n) is a finitely generated^-algebra if there exists a form SeP (a, b, c)(r) of n> 0 2 …

A toric ideal is called robust if its universal Gröbner basis is a minimal set of generators, and
is called generalized robust if its universal Gröbner basis equals its universal Markov basis …

A numerical semigroup is said to be universally free if it is free for any possible arrangement
of its minimal generating set. In this work, we establish that toric ideals associated with …

Minimal systems of generators for ideals of semigroups Page 1 JOURNAL OF PURE AND
APPLIED ALGEBRA ELSEVIER Journal of Pure and Applied Algebra 124 (1998) 7-30 Minimal …

The Hilbert function of a zero-dimensional ideal in a d-dimensional Cohen-Macaulay local
ring is studied when the depth of the associated graded ring of the ideal is at least d $-$1. In …

Let O be a monomial curve in the affine algebraic e-space over a field K and P be the
relation ideal of O. if O is defined by a sequence of e positive integers some e-1 of which …

Let k be a field and a< b< c be natural numbers. Let@: k [x. y, z]--+ k [t] be the
homomorphism defined by@(x)= ta, G (y)= tb. and@(z)= tc. The kernal of@ is called the …

Let be the monoid generated by We introduce the homogeneous catenary degree of as the
smallest N∈ ℕ with the following property: for each and any two factorizations u, v of a, there …