Generalized GCD rings II.
Generating ideals in local rings using elements of high degrees.
Generating Ideals in Polynomial Rings.
Geometry of superficial elements
Global structure of the mod two symmetric algebra, over the Steenrod Algebra.
Graded Cohen-Macaulay Rings Associated to Equimultiple Ideals.
Graded rings of complete intersection local rings with finite residue fields.
Graded transcendental extensions of graded fields.
Gröbner bases in geometry theorem proving and simplest degeneracy conditions.
Groupes de Picard et séries formelles
Groups with large Noether bound
The finite groups having an indecomposable polynomial invariant of degree at least half the order of the group are classified. It turns out that –apart from four sporadic exceptions– these are exactly the groups with a cyclic subgroup of index at most two.
Hilbert rings and the chain condition for prime ideals.
Homological properties of some Weyl algebra extensions
Homologie de Frobenius.
Homomorphismes discontinus des algèbres de Banach commutatives séparables
How to categorify one-half of quantum 𝔤𝔩(1|2)
We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra 𝔤𝔩(1|2).
Ideal class (semi)groups and atomicity in Prüfer domains
We explore the connection between atomicity in Prüfer domains and their corresponding class groups. We observe that a class group of infinite order is necessary for non-Noetherian almost Dedekind and Prüfer domains of finite character to be atomic. We construct a non-Noetherian almost Dedekind domain and exhibit a generating set for the ideal class semigroup.
Ideal theory in Prüfer rings with zero divisors.
Ideals in rings of integer valued polynomials.
Ideal-theoretic characterizations of valuation and Prüfer monoids
It is well known that an integral domain is a valuation domain if and only if it possesses only one finitary ideal system (Lorenzen -system of finite character). We prove an analogous result for root-closed (cancellative) monoids and apply it to give several new characterizations of Prüfer (multiplication) monoids and integral domains.