Putting emphasis on the relation between rational conformal field theory (RCFT) and algebraic number theory, we consider a brane configuration in which the D-brane intersection is an elliptic curve corresponding to RCFT. A new approach to the generation structure of fermions is proposed in which the flavor symmetry including the R-parity has its origin in the Galois group of elliptic curves wit...

Inheritance hierarchies often constitute the backbone of object-oriented systems. Their quality is therefore quite crucial. We present here our work the objective of which is to help designers to improve and to measure the quality of their inheritance hierarchies. The quality we deal with is the degree of factorization of information. Our work is based on the mathematical structure of Galois (c...

Let X be an arbitrary category with an (E,M)-factorization structure for sinks. A notion of constant morphism that depends on a chosen class of monomorphisms was previously used to provide a generalization of the connectedness-disconnectedness Galois connection (also called torsion-torsion free in algebraic contexts). This Galois connection was shown to factor throught the class of all closure ...

One of the fundamental questions in current field theory, related to Grothendieck’s conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classification of additive properties of multiplicative subgroups of fields containing all squares, using pro...

An abstraction is a property-preserving contraction of a program’s model into a smaller one that is suitable for automated analysis. An abstraction must be sound, and ideally, complete. Soundness and completeness arguments are intimately connected to the abstraction process, and approaches based on homomorphisms and Galois connections are commonly employed to define abstractions and prove their...

Given a finite group [Formula: see text], we study certain regular subgroups of the permutations which occur in classification theories two types algebraic objects: skew left braces with multiplicative isomorphic to text] and Hopf–Galois structures admitted by Galois extension fields text]. We questions when such yield or involving Hopf algebras. In particular, show that some cases isomorphism ...

Let X be an arbitrary category with an (E,M)-factorization structure for sinks. A notion of constant morphism that depends on a chosen class of monomorphisms is introduced. This notion yields a Galois connection that can be seen as a generalization of the classical connectedness-disconnectedness correspondence (also called torsion-torsion free in algebraic contexts). It is shown that this Galoi...

The orthomorphism on the Galois field is a kind of permutations that is the most widely used in crosscutting issue, the orthomorphic polynomials over the finite field is an effective method to study it, this study has obtained the coefficients relationship of the orthomorphisms over the Galois field by algebraic methods. In addition, this study have understood the maximal subgroup structure and...

Let A be a ring with identity. The generalized affine transformation monoid Gaff(A) is defined as the set of all transformations on A of the form x → xu + a (for all x ∈ A), where u,a∈ A. We study the algebraic structure of the monoid Gaff(A) on a finite Galois ring A. The following results are obtained: an explicit description of Green’s relations on Gaff(A); and an explicit description of the...

We define and study certain moduli stacks of modules equipped with a Frobenius semi-linear endomorphism. These stacks can be thought of as parametrizing the coefficients of a variable Galois representation and are global variants of the spaces of Kisin–Breuil Φ-modules used by Kisin in his study of deformation spaces of local Galois representations. A version of a rigid analytic period map is d...