Related papers: Intersection properties of relations
We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solutions to these equations with coordinates in algebraically…
In this paper we prove several theorems about the behavior of index of Lie algebras derived from associative algebras under tensor products of underlying associative algebras.
In \cite{Cho09}, Choi studied congruences of coefficients (modulo $T^q-T$) for Drinfeld modular forms of level $\Gamma_0(T)$, trivial type and the linear relations between the initial coefficients of those. In this article, we generalize…
We consider the intersection $\mathfrak{M}(A)$ of all maximal ideals of an evolution algebra $A$ and study the structure of the quotient $A/\M(A)$. In a previous work, maximal ideals have been related to hereditary subsets of a graph…
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
We prove congruence relations modulo cyclotomic polynomials for multisums of $q$-factorial ratios, therefore generalizing many well-known $p$-Lucas congruences. Such congruences connect various classical generating series to their…
We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra.
An amorphic association scheme has the property that any of its fusion is also an association scheme. In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up…
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…
We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group.…
The purpose of this paper is to consider when two maximal subalgebras of a finite-dimensional solvable Lie algebra $L$ are conjugate, and to investigate their intersection.
We initiate the study of reducts of relational structures up to primitive positive interdefinability: After providing the tools for such a study, we apply these tools in order to obtain a classification of the reducts of the logic of…
We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible products on null-filiform associative algebras.
It is known that any square matrix over any field F is congruent to its transpose. We show that they are also *congruent with respect to any nonidentity involution on F.
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…
We study intersection theory for differential algebraic varieties. Particularly, we study families of differential hypersurface sections of arbitrary affine differential algebraic varieties over a differential field. We prove the…
We first establish several general properties of modality of algebraic group actions. In particular, we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we…
We give an accessible introduction into the theory of lower central series of associative algebras, exhibiting the interplay between algebra, geometry and representation theory that is characteristic for this subject, and to discuss some…
We give necessary and sufficient conditions for zigzag algebras and certain generalizations of them to be (relative) cellular, quasi-hereditary or Koszul.
We study possibilities of preservations for properties, their links and related connections between semantic and syntactic ones, both in general and as characterizations for subalgebras, congruence relations, Henkin construction,…