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Fuzzy Rees congruences on semigroups

✍ Scribed by Xiang-Yun Xie

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 394 KB
Volume: 102
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(97)00156-5

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✦ Synopsis

Fuzzy congruences on semigroups and groups have been introduced and studied by and , among others. Here, we introduce fuzzy Rees congruences on semigroups and fuzzy Rees congruences semigroups. Using these ideas, we establish a relation between fuzzy ideals of a semigroup S and fuzzy ideals of a quotient semigroup of S. As an important result, we prove that the lattice of all fuzzy congruences on a fuzzy congruences semigroup is a distributive lattice. Moreover, we obtain that a homomorphic image of a fuzzy Rees congruences semigroup is a fuzzy Rees congruences semigroup, as well.

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