Some Results on Stabilizers in Residuated Lattices

Abstract

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.

Keywords

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

References

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