This book contains the definitions of several ring constructions used in various applications.
The concept of a groupoid-graded ring includes many of these constructions as special …

For an integral domain R and a commutative cancellative monoid M, the ring consisting of all
polynomial expressions with coefficients in R and exponents in M is called the monoid ring …

In this paper, a semigroup algebra consisting of polynomial expressions with coefficients in
a field F and exponents in an additive submonoid M of Q≥ 0 is called a Puiseux algebra …

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 …

In this paper we study those submonoids of N^ d N d with a nontrivial pseudo-Frobenius set.
In the affine case, we prove that they are the affine semigroups whose associated algebra …

Let S be a cancelative finitely generated commutative semigroup satisfying the property S c3
(-S)=(0)(the last condition will be referred as combinatorially finite in the sequel). Fix a finite …

In this paper, we deal with the problem of the uniqueness of a minimal system of binomial
generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient …

Let $ G $ be a finite graph and $ K [G] $ the edge ring of $ G $. Based on the technique of
Gröbner bases and initial ideals, it will be proved that, given integers $ f $ and $ d $ with …

This paper is concerned with the combinatorial description of the graded minimal free
resolution of certain monomial algebras which includes toric rings. We explicitly describe …

Let k be an arbitrary field and let b> 1, n> 1 and a be three positive integers. In this paper we
explicitly describe a minimal S-graded free resolution of the semigroup algebra k [S] when S …