Related papers: On computable field embeddings and difference clos…

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…

We study the degrees of selector functions related to the degrees in which a rigid computable structure is relatively computably categorical. It is proved that for some structures such degrees can be represented as the unions of upper cones…

We investigate the computability of algebraic closure and definable closure with respect to a collection of formulas. We show that for a computable collection of formulas of quantifier rank at most $n$, in any given computable structure,…

Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…

The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…

We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…

We exhibit a connection between two constructions of twisted modules for a general vertex operator algebra with respect to inner automorphisms. We also study pseudo-derivations, pseudo-endomorphisms, and twist deformations of ordinary…

We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.

Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…

Let G be a reductive algebraic group over a number field k. It is shown how Emerton's methods may be applied to the problem of p-adically interpolating the metaplectic forms on G, i.e. the automorphic forms on metaplectic covers of G, as…

In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the…

We classify the algebraic combinatorial geometries of arbitrary field extensions of transcendence degree greater than 4 and describe their groups of automorphisms. Our results and proofs extend similar results and proofs by Evans and…

Nearly all practical applications of the theory of characteristic modes (CMs) involve the use of computational tools. Here in Paper 2 of this Series on CMs, we review the general transformations that move CMs from a continuous theoretical…

We continue the study of computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a…

This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…

Embedding spaces contain interpretable dimensions indicating gender, formality in style, or even object properties. This has been observed multiple times. Such interpretable dimensions are becoming valuable tools in different areas of…

Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…

Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…

We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding…