This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the "sum" of two elements is a subset of the structure. The results in this paper show that these structures .cannot always be embedded in the decomposition of an ordinary structure (ring or field) in equivalence classes and that the structural results for hyperfields and...

The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (m, n)-hyperring R such that the quotient space is an (m, n)-ring, to introdu...

Purpose The purpose of this study was to examine the effect of a Mind-Body Medicine program for enhancing self-care and well-being among first year medical students. Depression and anxiety are common among medical students (West et al, 2011) and physicians (Krasner et al, 2009). Further, distress among medical students is associated with poor patient care (Dyrbye et al, 2010; Krasner et al, 200...

The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization cyclic In this paper, we study over finite Krasner hyperfields which characterize them by their generating polynomial. Moreover, dual these finding parity check

In this paper, our aim is to generalize and extend the Hopkins-Levitzki theorem from noncommutative rings Krasner hyperring. Also, we prove that a hyperring R Noetherian if only it satisfies ascending chain conditions of prime hyperideals.