The hyperfield came into being due to a mathematical necessity that appeared during the study of the valuation theory of the fields by M. Krasner, who also defined the hyperring, which is related to the hyperfield in the same way as the ring is relat...
We study the notions of the positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We demonstrate how these interact in order to produce interesting results in the theory of hyperfields. For instance, we provide a criterion for...
In this paper, we introduce generalized homographic transformations as hyperhomographies over Krasner hyperfields.These particular algebraic hyperstructues are quotient structures of classical fields modulo normal groups. Besides, we define some hype...
Valuation theory is an important area of investigation in algebra, with applications in algebraic geometry and number theory. In 1957, M. Krasner introduced hyperfields, which are field-like objects with a multivalued addition, to describe some struc...
In 1957, M. Krasner described a complete valued field
In this paper, we introduce generalized quadratic forms and hyperconics over quotient hyperfields as a generalization of the notion of conics on fields. Conic curves utilized in cryptosystems; in fact the public key cryptosystem is based on the digit...
The various branches of Mathematics are not separated between themselves. On the contrary, they interact and extend into each other’s sometimes seemingly different and unrelated areas and help them advance. In this sense, the Hypercompositional...
A Krasner hyperring (for short, a hyperring) is a generalization of a ring such that the addition is multivalued and the multiplication is as usual single valued and satisfies the usual ring properties. One of the important subjects in the theory of...
Research on failure mechanism is essential for the prolonging of gun barrel lifetime. To explore the gun barrel failure mechanism, the damage characteristics of a machine gun barrel were characterized. The results show that the failure of the gun bar...
Inspired by the concept of regular local rings in classical algebra, in this article we initiate the study of the regular parameter elements in a commutative local Noetherian hyperring. These elements provide a deep connection between the dimension o...
Hyper-field effect transistors (hyper-FETs) are crucial in the development of low-power logic devices. With the increasing significance of power consumption and energy efficiency, conventional logic devices can no longer achieve the required performa...