Some Results on Stabilizers in Residuated Lattices

Yıl 2014, Cilt: 11 Sayı: 2, - , 01.11.2014

Masoud Haveshki

Öz

Borumand and Mohtashamnia in [1] introduced the notion of the (right and left) stabilizer in
residuated lattices and proved some theorems which determine the relationship between this notion and some
types of filters in residuated lattices. In this paper, we show that a part of Theorem 3.10 [1] is not correct.
Borumand and Mohtashamnia proved Theorem 4.2 [1] with some conditions. We prove this theorem without
any condition. Also, we prove Theorem 3.8 and part (4) of Proposition 3.3 in [1] more generally and finally
obtain some new and useful theorems on stabilizers in residuated lattices.

Anahtar Kelimeler

Residuated lattices, stabilizer, implicative filter, positive implicative filter, fantastic filter, obstinate filter.

Kaynakça

• [1] A. Borumand Saeid, N. Mohtashamnia, Stabilizer in residuated lattices, University Politehnica of Bucharest, Scientific Bulletin Series A - Applied Mathematics and Physics, 74(2), (2012), 65–74.
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• [4] C. Muresan, Dense Elements and Classes of Residuated Lattices, Bull. Math. Soc. Sci. Math. Roumanie Tome, 53(101)(1), (2010), 11–24.
• [5] D. Piciu, Algebras of Fuzzy Logic, Ed. Universitaria Craiova, (2007).
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