$N$-hyperideals and related extensions
Abstract
Various classes of hyperideals have been studied in many papers in order to let us fully understand the structures of hyperrings in general. The purpose of this paper is the study of some hyperideals whose concept is created on the basis of the intersection of all $n$-ary prime hyperideals in category of Krasner $(m, n)$-hyperrings. In this regard we introduce notions of $N$-hyperideals, $\delta$-$N$-hyperideals, $(k,n)$-absorbing $\delta$-$N$-hyperideals and $S$-$N$-hyperideals. The overall framework of these structures is then explained, providing a number of major conclusions.
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