Related papers: On Algebraic properties of ABO-Blood Type Inherita…
The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic…
There is an extensive recent literature on the graded, non-graded, prime, primitive, maximal ideals of Leavitt path algebras. In this introductory level survey, we will be giving an overview of different types of ideals and the…
We study the congeniality property of algebras, as defined by Bao, He, and Zhang, in order to establish a version of Auslander's theorem for various families of filtered algebras. It is shown that the property is preserved under homomorphic…
We prove that the lattice of ideals of an arbitrary $L$-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of $L$-algebras and characterize…
We deal with the existing problem of filtered multiplicative bases of finite-dimensional associative algebras. For an associative algebra A over a field, we investigate when the property of having a filtered multiplicative basis is…
In this article, we introduce a relation including ideals of an evolution algebra and hereditary subsets of vertices of its associated graph and establish some properties among them. This relation allows us to determine maximal ideals and…
We give a complete closed form description of the evolution of human blood genotypes frequencies (in the ABO and Rh classification) after any (finite or infinite) number of generations and for any initial distribution.
The notion of the characteristic Lie algebra of the discrete hyperbolic type equation is introduced. An effective algorithm to compute the algebra for the equation given is suggested. Examples and further applications are discussed.
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
We associate to each synchronous game an algebra whose representations determine if the game has a perfect deterministic strategy, perfect quantum strategy or one of several other perfect strategies. when applied to the graph coloring game,…
In this paper we focus on the structure of the variety of Lie algebras with a finite number of ideals and their graph representations using Hasse diagrams. The large number of necessary conditions on the algebraic structure of this type of…
Abstract algebra provides a large hierarchy of properties that a collection of objects can satisfy, such as forming an abelian group or a semiring. These classifications can arranged into a broad and typically acyclic directed graph. This…
A mechanism for the inheritance of properties of spectra by differential spectra is developed and applied to prove geometric properties of morphisms of differential algebraic varieties.
Hom-algebras are generalizations of algebras obtained using a twisting by a linear map. But there is a priori a freedom on where to twist. We enumerate here all the possible choices in the Lie and associative categories and study the…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
We investigate subshifts with a general algebraic structure and cellular automata on them, with an emphasis on (order-theoretic) lattices. Our main results concern the characterization of Boolean algebraic subshifts, conditions for…
Many natural populations are well modelled through time-inhomogeneous stochastic processes. Such processes have been analysed in the physical sciences using a method based on Lie algebras, but this methodology is not widely used for models…
We investigate the defining ideal of the algebra over a field generated by the join-meet binomials coming from a finite distributive lattice. In the frame of algebras with straightening laws, the problem when the defining ideal is generated…
We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the `blob' algebra (the reason for the…
The ABO histo-blood group, the critical determinant of transfusion incompatibility, was the first genetic polymorphism discovered in humans. Remarkably, ABO antigens are also polymorphic in many other primates, with the same two amino acid…