Related papers: Special Algebraic Structures
In this article we shows some results about algebra with the group of units having special polynomial identity.
We study several different notions of algebraicity in use in stable homotopy theory and prove implications between them. The relationships between the different meanings of algebraic are unexpectedly subtle, and we illustrate this with…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
We investigate the algebra of an ample groupoid, introduced by Steinberg, over a semifield S. In particular, we obtain a complete characterization of congruence-simpleness for Steinberg algebras of second-countable ample groupoids,…
We survey recent applications of topology and singularity theory in the study of the algebraic complexity of concrete optimization problems in applied algebraic geometry and algebraic statistics.
In a recent work we have shown how to construct an information algebra of coherent sets of gambles defined on general possibility spaces. Here we analyze the connection of such an algebra with the set algebra of subsets of the possibility…
We study possibilities for algebraic closures, differences between definable and algebraic closures in first-order structures, and variations of these closures with respect to the bounds of cardinalities of definable sets and given sets of…
A theory of cyclic elements in semisimple Lie algebras is developed. It is applied to an explicit construction of regular elements in Weyl groups.
We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.
In the paper "An Abelian Loop for Non-Composites" (arXiv:110.14716), we introduced a group-like structure consisting of odd prime numbers and 1, with properties that allowed us to prove analogous results to well known theorems in Number…
The connection between q-analogs of special functions and representations of quantum algebras has been developed recently. It has led to advances in the theory of q-special functions that we here review.
Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…
In 2011, a topic containing the concepts of upper and lower periodic subsets of (basic) algebraic structures was introduced and studied. The concept of ``upper periodic subsets'' can be considered as a generalized topic of ideals and…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Hypergroups are lifted to power semigroups with negation, yielding a method of transferring results from semigroup theory. This applies to analogous structures such as hypergroups, hyperfields, and hypermodules, and permits us to transfer…
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical…
Generally the study of algebraic deals with the concepts like groups, semigroups, groupoids, loops, rings, near-rings, semirings and vector spaces. The study of bialgebraic structures deals with the study of bistructures like bigroups,…