Product of fuzzy \(H_v\)-ideals in \(H_v\)-rings (Q2761624)

The author continues his study on fuzzy \(H_v\)-structures [\textit{B. Davvaz}, J. Fuzzy Math. 6, No. 1, 33-42 (1998; Zbl 0902.16040), Fuzzy Sets Syst. 101, No. 1, 191-195 (1999; Zbl 0935.20065), J. Fuzzy Math. 8, No. 1, 43-51 (2000; Zbl 0957.20054)], where in the axioms the equality is replaced by the non-empty intersection. The paper focuses on products of fuzzy \(H_v\)-ideals defined on \(H_v\)-rings in a natural way. If \((R,+,\cdot)\) is an \(H_v\)-ring, the fundamental relation \(\gamma^*\) on an \(H_v\)-ring is defined as the smallest equivalence relation on \(R\) such that the quotient \(R/\gamma^*\) is a ring, the so called fundamental ring. Finally, the behavior of the fundamental relations and fundamental rings with respect to the product of fuzzy \(H_v\)-ideals is investigated.