Manis valuations and Prüfer extensions
Manis valuations and Prüfer extensions. I.
Matroids over a ring
We introduce the notion of a matroid over a commutative ring , assigning to every subset of the ground set an -module according to some axioms. When is a field, we recover matroids. When , and when is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, i.e. tropical linear spaces, respectively. More generally, whenever is a Dedekind domain, we extend all the usual properties and operations holding for matroids (e.g., duality), and...
Maximal non valuation domains in an integral domain
Let be a commutative ring with unity. The notion of maximal non valuation domain in an integral domain is introduced and characterized. A proper subring of an integral domain is called a maximal non valuation domain in if is not a valuation subring of , and for any ring such that , is a valuation subring of . For a local domain , the equivalence of an integrally closed maximal non VD in and a maximal non local subring of is established. The relation between and the number...
Maximal non-Jaffard subrings of a field.
A domain R is called a maximal non-Jaffard subring of a field L if R ⊂ L, R is not a Jaffard domain and each domain T such that R ⊂ T ⊆ L is Jaffard. We show that maximal non-Jaffard subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dimv R = dim R + 1. Further characterizations are given. Maximal non-universally catenarian subrings of their quotient fields are also studied. It is proved that this class of domains coincides with the previous class when R is integrally...
Maximality properties for one-dimensional analytically irreducible local Gorenstein and Kunz rings.
Minimal degree solutions of polynomial equations
Minimal sets of generators for the relation ideals of certain monomial curves.
Minimale Erzeugendensystem und minimale Primteiler von monomialen Radikalidealen.
Mittag-Leffler modules and semi-hereditary rings
Models of group schemes of roots of unity
Let be a discrete valuation ring of mixed characteristics , with residue field . Using work of Sekiguchi and Suwa, we construct some finite flat -models of the group scheme of -th roots of unity, which we call Kummer group schemes. We carefully set out the general framework and algebraic properties of this construction. When is perfect and is a complete totally ramified extension of the ring of Witt vectors , we provide a parallel study of the Breuil-Kisin modules of finite flat models...
Modular quadratic and Hermetian forms over Dedekind rings. I.
Modular quadratic and Hermitian forms over Dedekind rings.
Modules réflexifs et anneaux factoriels
Moduli space of filtered -ring structures over a filtered ring.
Monomial Buchsbaum ideals in Ipr.
Monomial Gorenstein Ideals.
Monomial ideals with 3-linear resolutions
In this paper, we study the Castelnuovo-Mumford regularity of square-free monomial ideals generated in degree . We define some operations on the clutters associated to such ideals and prove that the regularity is preserved under these operations. We apply these operations to introduce some classes of ideals with linear resolutions and also show that any clutter corresponding to a triangulation of the sphere does not have linear resolution while any proper subclutter of it has a linear resolution....
Monomial ideals with tiny squares and Freiman ideals
We provide a construction of monomial ideals in such that , where denotes the least number of generators. This construction generalizes the main result of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018). Working in the ring , we generalize the definition of a Freiman ideal which was introduced in J. Herzog, G. Zhu (2019) and then we give a complete characterization of such ideals. A particular case of this characterization leads to some further investigations on that generalize some results...
Monominal ideal residue class rings and iterated Golod maps.