in this paper we will generalize  some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .

The study of dihedral f-tilings of the Euclidean sphere S2 by triangles and rsided regular polygons was initiated in 2004 where the case r = 4 was considered [5]. In a subsequent paper [1], the study of all spherical f-tilings by triangles and r-sided regular polygons, for any r ≥ 5, was described. Later on, in [3], the classification of all f-tilings of S2 whose prototiles are an equilateral t...

$!!!!$ in this paper, the notion of fuzzy $!$ krasner $!(m, n)$-hyperrings($!f^{(m, n)}!$-hyperrings) by using the notion of$f^m$-hyperoperations and $f^n$-operations is introduced and somerelated properties are investigated. in this regards,relationships between krasner $f^{(m, n)}$-hyperrings and krasner$(m, n)$-hyperrings are considered. we shall prove that everykrasner $f^{(m, n)}$-hyperrin...