Fuzzy Integral domains and Fuzzy regular sequences

In this paper, the notions of fuzzy zero-divisors and fuzzy integral domains are illustrated. Some fundamental properties of fuzzy integral domains are proved. Moreover, the notions of fuzzy regular element and fuzzy regular sequences are defined. It is shown that any permutation (resp. any positive integral power) of a fuzzy regular sequence is again a fuzzy regular sequence. At the end, fuzzy regular sequences of two fuzzy submodules are related with the help of fuzzy short exact sequences.