In this paper we will introduce the notion of coprime hyperideals in multiplicative hyperrings and we will show some properties of them. Then we introduce the notion of hyperring of fractions generated by a multiplicative hyperring and then we will show some properties of them.
In this paper we observe that, the notions of (m, n)-fold p-ideals and fuzzy (m, n)-fold p-ideals, for each positive integers m, n, are indeed the natural generalization of p-ideals and fuzzy p-ideals, respectively. A characterization of (m, n)-fold p-ideals and fuzzy (m, n)-fold p-ideals is given, and conditions for which an ideal (respectively fuzzy ideal) is an (m, n)-fold p-ideal (respectively fuzzy (m, n)-fold p-ideal) are studied. We also establish extension properties for (m, n)-fold p-ideals and fuzzy (m, n)-fold p-ideals. Furthermore, we construct some algorithms to determine whether certain finite sets provided with a well defined operation, are BCI-algebras, (m, n)-fold p-ideals, fuzzy subsets or fuzzy (m, n)-fold p-ideals.
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