The various structures of fuzzy quotient modules (Q1311783)

The author introduces three definitions of fuzzy quotient modules (i) for an arbitrary fuzzy module and its fuzzy submodule, (ii) for an arbitrary fuzzy divisible module and its fuzzy prime submodule, (iii) for an arbitrary fuzzy module and its strong \(p\)-level fuzzy submodule. Also, two kinds of fuzzy quotient vector space \(\overline\eta_{v/w}\), \(\check\eta_{v/w}\) are constructed for any fuzzy vector space \(V\) and its arbitrary fuzzy vector subspace \(W\), and \(\overline\eta_{v/w}=\check\eta_{v/w}\) is proved when \(W=V_ p\) or \(W=V^ p\).