Abstract
We study some special sets in MTL-algebras. The notion of the radical of a filter in MTL-algebras is defined and several characterizations of the radical of a filter are given. The sets of dense elements and double complemented elements in MTL-algebras are defined and we state and prove some theorems on the properties of these sets and filters of MTL-algebras. We also prove that the radical of a positive implicative filter of an MTL-algebra is a subset of double complemented elements.
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