Related papers: Fundamental relations in multialgebras. Applicatio…
We propose a new class of algebraic structure named as \emph{$(m,n)$-semihyperring} which is a generalization of usual \emph{semihyperring}. We define the basic properties of $(m,n)$-semihyperring like identity elements, weak distributive…
Planar linkages are a rich area of study motivated by practical applications in engineering mechanisms. A central result is Kempe's Universality Theorem, which states that semi-algebraic sets can be realized by planar linkages. Polyhedral…
For a given extension $A \subset E$ of associative algebras we describe and classify up to an isomorphism all $A$-complements of $E$, i.e. all subalgebras $X$ of $E$ such that $E = A + X$ and $A \cap X = \{0\}$. Let $X$ be a given…
Assuming complex functions defined on complex curves satisfy recursion relations with respect to number of parameters, we express the corresponding cohomology theory via generalizations of holomorphic connections. In examples provided, the…
The following article is an application of commutative algebra to the study of multiparameter persistent homology in topological data analysis. In particular, the theory of finite free resolutions of modules over polynomial rings is applied…
By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…
We give an introduction to the study of algebraic hypersurfaces, focusing on the problem of when two hypersurfaces are isomorphic or close to being isomorphic. Working with hypersurfaces and emphasizing examples makes it possible to discuss…
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…
We consider several distinct characterizations of finite implication algebras. One of these leads to a new characterization of Boolean polymatroids.
We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
Monogamy and polygamy of quantum correlations are the fundamental properties of quantum systems. We study the monogamy and polygamy relations satisfied by any quantum correlations in multipartite quantum systems. General monogamy relations…
We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…
The notion of associativity (which differs from the straightforward generalization of the usual associativity given by the move of parentheses in the relevant expression) for operations of high arity is introduced. It is proved that the…
It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…
We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the…
Binary multirelations can model alternating nondeterminism, for instance, in games or nondeterministically evolving systems interacting with an environment. Such systems can show partial or total functional behaviour at both levels of…
We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…
We elaborate on the consequences of the factorization of the transfer matrix of any lossless multilayer in terms of three basic matrices of simple interpretation. By considering the bilinear transformation that this transfer matrix induces…
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.