FOUNDATIONS OF ORDERED (SEMI)HYPERRINGS - Davvaz, Bijan; Omidi, S. (IndoMS, 2016)
In this paper, we introduce the notion of general hyperring (R,+,·) besides a binary relation , where is a partial order such that satisfies the conditions: (1) If a b, then a+c b+c, meaning that for any x a+c, there exists y b+c such that xy. The case c+ac+b is defined similarly. (2) If a b and c R, then a· c b· c, meaning that for any xa· c, there exists yb· c such that xy. The case c· a c· b is defined similarly. This structure is called an ordered general hyperring. Also, we present several examples of ordered general hyperrings and prove some results in this respect. By using the notion of pseudoorder on an ordered general hyperring (R,+,·,), we obtain an ordered ring. Moreover, we study some properties of pseudoorder on an ordered general hyperring.DOI :Â http://dx.doi.org/10.22342/jims.22.2.233.131-150