A note on “New fundamental relation of hyperrings”.

Abstract: In the theory of hyperrings, fundamental relations make a connection between hyperrings and ordinary rings. Commutative fundamental rings and the fundamental relation which is the smallest strongly regular relation in hyperrings were introduced by Davvaz and Vougiouklis (2007). Recently, another strongly regular relation named on hyperrings has been studied by Ameri and Norouzi (2013). Ameri and Norouzi proved that is the smallest strongly regular relation such that is a commutative ring. In this paper, we show that and is not the smallest strongly regular relation. Moreover, we show that some results of Ameri and Norouzi do not hold. [Copyright &y& Elsevier]