Text. We show that the theory of hyperrings, due to M. Krasner, supplies a perfect framework to understand the algebraic structure of the adèle class space H K = A K /K × of a global field K. After promoting F 1 to a hyperfield K, we prove that a hyperring of the form R/G (where R is a ring and G ⊂ R × is a subgroup of its multiplicative group) is a hyperring extension of K if and only if G ∪ {0} is a subfield of R. This result applies to the adèle class space which thus inherits the structure of a hyperring extension H K of K. We begin to investigate the content of an algebraic geometry over K. The category of commutative hyperring extensions of K is inclusive of: commutative algebras over fields with semi-linear homomorphisms, abelian gro...
“Ends Lemma” is used to construct a hypergroupoid from a (quasi) partially ordered groupoid. But thi...
In this paper we introduce a class of hyperfields which contains non quotient hyperfields. Thus we g...
Abstract. Assuming some basic knowledge of groups, rings, and fields, the following investigation wi...
Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, b...
AbstractTextWe show that the theory of hyperrings, due to M. Krasner, supplies a perfect framework t...
The hyperfield came into being due to a mathematical necessity that appeared during the study of the...
This survey article presents some recent results in the theory of hyperfields and hyperrings, algebr...
AbstractLet k be a number field and Ok its ring of integers. Let l be a prime number and m a natural...
AbstractThe aim of this research work is to define and characterize a new class of n-ary multialgebr...
By a hyperring we mean a structure (A,⊕, ◦) where (A,⊕) is a hy-pergroup, (A, ◦) is a semihypergroup...
Title: Algebraic Substructures in ℂ Author: Vítězslav Kala Department: Department of Algebra Supervi...
In this thesis we present the main theorems of global class field theory stated in terms of ideals a...
Multialgebraic structures -- an "algebraic like" structure but endowed with multiple valued operatio...
This paper falls in the area of hypercompositional algebra. In particular, it focuses on the class o...
Numbers, Polynomials, and Factoring The Natural Numbers The Integers Modular Arithmetic Polynomials ...
“Ends Lemma” is used to construct a hypergroupoid from a (quasi) partially ordered groupoid. But thi...
In this paper we introduce a class of hyperfields which contains non quotient hyperfields. Thus we g...
Abstract. Assuming some basic knowledge of groups, rings, and fields, the following investigation wi...
Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, b...
AbstractTextWe show that the theory of hyperrings, due to M. Krasner, supplies a perfect framework t...
The hyperfield came into being due to a mathematical necessity that appeared during the study of the...
This survey article presents some recent results in the theory of hyperfields and hyperrings, algebr...
AbstractLet k be a number field and Ok its ring of integers. Let l be a prime number and m a natural...
AbstractThe aim of this research work is to define and characterize a new class of n-ary multialgebr...
By a hyperring we mean a structure (A,⊕, ◦) where (A,⊕) is a hy-pergroup, (A, ◦) is a semihypergroup...
Title: Algebraic Substructures in ℂ Author: Vítězslav Kala Department: Department of Algebra Supervi...
In this thesis we present the main theorems of global class field theory stated in terms of ideals a...
Multialgebraic structures -- an "algebraic like" structure but endowed with multiple valued operatio...
This paper falls in the area of hypercompositional algebra. In particular, it focuses on the class o...
Numbers, Polynomials, and Factoring The Natural Numbers The Integers Modular Arithmetic Polynomials ...
“Ends Lemma” is used to construct a hypergroupoid from a (quasi) partially ordered groupoid. But thi...
In this paper we introduce a class of hyperfields which contains non quotient hyperfields. Thus we g...
Abstract. Assuming some basic knowledge of groups, rings, and fields, the following investigation wi...