Hyperstructures of affine algebraic group schemes

Neutrosophic quadruple algebraic hyperstructures

The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them. 2010 AMS Classification: 03B60, 20A05, 20N20, 97H40

One - Dimensional Affine Group Schemes

The construction of these groups is straightforward; to an algebra B we assign the quotient R,,, G,/G,. The main effort comes in showing that these are the only possibilities. The key to this, and the basic technical idea in the paper, is the use of N&on blow-ups of group schemes over valuation rings. This process has been used before [ 1, 21 as a tool for resolving singularities, but in fact i...

Chemical salt reactions as algebraic hyperstructures

A salt metathesis reaction is a chemical process involving the exchange of bonds between two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations. Hyperstructure theory is studied from the theoretical point of view and for its applications. In this paper, we provide some examples of hyperstructures associated with salt m...

Basic Theory of Affine Group Schemes

Algebraic Monoids with Affine Unit Group Are Affine

In this short note we prove that any irreducible algebraic monoid whose unit group is an affine algebraic group is affine.