Related papers: Difference Nullstellensatz
We give a short proof of the most general version of the Nullstellensatz without using the Axiom of Choice.
Motivated by pseudo-Gorenstein rings in commutative algebra, introduced by Herzog et al., we define pseudo-Gorenstein$^{*}$ graphs and classify them in several natural graph families using independence polynomials.
A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis,…
Quasi-set theory is a first order theory without identity, which allows us to cope with non-individuals in a sense. A weaker equivalence relation called ``indistinguishability'' is an extension of identity in the sense that if $x$ is…
We construct an invariant of t-structures on the derived category of a Noetherian ring. This invariant is complete when restricting to the category of quasi-coherent complexes, and also gives a classification of nullity classes with the…
Outside of the framework of geometric theories, we exhibit complete, respectively model-complete theories of rings whose corresponding theory of pairs is complete, respectively model-complete, using transfer results proven in the seventies…
String Field Theory is a formulation of String Theory as a Quantum Field Theory in target space. It allows to tame the infrared divergences of String Theory and to approach its non-perturbative structure and background independence. This…
We define and describe the properties of a class of perverse sheaves which is very useful when the base ring is not a field.
The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define this ring axiomatically, by generators and defining…
We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another.…
Improved local and global versions of the effective Nullstellensatz for ideal sheaves on non-singular complex varieties are obtained, based on a new invariant motivated by the notion of finite type from the theory of several complex…
The dressing field method is a tool to reduce gauge symmetries. Here we extend it to cover the case of diffeomorphisms. The resulting framework is a systematic scheme to produce Diff(M)-invariant objects, which has a natural relational…
The theory of difference-differential fields of characteristic zero has a model-companion denoted by $\it DCFA$. Previously we proved a weak version of Zilber's dichotomy for $\it DCFA$. In this paper we use arc spaces techniques as…
We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on the space of partially labeled points on…
An integro-differential ring is a differential ring that is closed under an integration operation satisfying the fundamental theorem of calculus. Via the Newton--Leibniz formula, a generalized evaluation is defined in terms of integration…
In the framework of the Relativistic Mean Field Approach a pseudospin dependence of the residual forces in nuclei is considered. It is shown that this dependence is relatively weak. As a consequence, a pseudospin dependence of the…
Automorphic loops are loops in which all inner mappings are automorphisms. This variety of loops includes groups and commutative Moufang loops. A half-isomorphism $f : G \longrightarrow K$ between multiplicative systems $G$ and $K$ is a…
Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B contained in A which is embedded with a stronger structure S. These types of structures occur in our…
In this article, we introduce pseudo-absolute values, which generalise usual absolute values. Roughly speaking, a pseudo-absolute value on a field $K$ is a map $|\cdot| : K \to [0,+\infty]$ satisfying axioms similar to those of usual…