On the lattice of fuzzy ideals of a ring

✍ Scribed by Qingde Zhang; Guangwu Meng

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 80 KB
• Volume: 112
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(98)00234-6

✦ Synopsis

First, we prove that ∨ Á = + Á in the lattice of all fuzzy (left, right) ideals with the same tip "t" using the technique of strong cut. By this we obtain the following results: (1) We point out that the lattice of all fuzzy ideals of a ring is not distributive, thus the main theorem (L F1(R) is distributive) in Majumdar and Sultana (1996) is erroneous. (2) The lattice of all fuzzy (left, right) ideals with same tip "t", of a ring R is modular, this generalizes the main theorem in Ajmal and Thomas (1995).