A note on "New fundamental relation of hyperrings"

作者：Mirvakili S^*; Davvaz B; Fotea V Leoreanu

来源：European Journal of Combinatorics, 2014, 41: 258-261.

DOI：10.1016/j.ejc.2014.04.004

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

• 出版日期2014-10