相关论文: Completeness of translation-invariant ideals in gr…
We introduce and prove the consistency of a new set theoretic axiom we call the \emph{Invariant Ideal Axiom}. The axiom enables us to provide (consistently) a full topological classification of countable sequential groups, as well as fully…
We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.
In this paper, we define an invariant, which we believe should be the substitute for total K-theory in the case when there is one distinguished ideal. Moreover, some diagrams relating the new groups to the ordinary K-groups with…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
We will show that group exactness is a von Neumann equivalence invariant. This result generalizes the previously known fact stating that group exactness is invariant under measure equivalence and W*-equivalence.
Let $\mathrm{SO}^+(p,q)$ denote the identity connected component of the real orthogonal group with signature $(p,q)$. We give a complete description of the spaces of continuous and generalized translation- and $\mathrm{SO}^+(p,q)$-invariant…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
Consideration of certain properties of group rings and their ideals search
We prove two isomorphism-invariance theorems for groupoids associated with ultragraphs. These theorems characterize ultragraphs for which the topological full group of an associated groupoid is an isomorphism invariant. These results extend…
In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative…
We prove completeness for the main examples of infinite-dimensional Lie groups and some related topological groups.
In this paper the concept of extension of a Q-fuzzy ideal in semigroups has been introduced and some important properties have been studied.
This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…
We introduce the notion of a transformation digroup and prove that every digroup is isomorphic to a transformation digroup.
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…
We introduce a new graph invariant of finite groups that provides a complete characterization of the splitting types of unramified prime ideals in normal number field extensions entirely in terms of the Galois group. In particular, each…
We introduce a new concept in the Absorbing Ideal Theory in commutative rings, that is, the $\omega$-stable groups. We will provide examples and non-examples of these groups, and establish their relationship with H-congruence. Ultimately,…
We introduce a two-parameter modification of the cofinality invariant of ideals. This allows us to include the interaction of a pair of ideals in the study of base-like structures. We find the values (cardinal numbers or well-known cardinal…
In this paper we describe the Greens relations on the semigroup of bi-ideals of ordered full transformation semigroup in terms of Greens relations of ordered full transformation semigroup on a set.
A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar…