Abstract
In this paper, we explore the existence of nontrivial monadic operators on linearly ordered monadic nilpotent minimum algebras (NM-algebras, for short) and achieve the necessary and sufficient conditions for a linearly ordered monadic NM-algebra having monadic operators. We verify that each finite linearly ordered monadic NM-algebra with more than 4 elements has nontrivial monadic operators. We study the simple and subdirectly irreducible monadic NM-algebras and derive the necessary and sufficient conditions for a monadic NM-algebra to be simple and subdirectly irreducible, respectively. In addition, we discuss finite monadic involutive monoidal t-norm based algebras (IMTL-algebras, for short) and give some examples to show that there exist finite linearly ordered monadic IMTL-algebras having only trivial monadic operators. We establish the conditions for finite linearly ordered perfect monadic IMTL-algebras having nontrivial monadic operators.
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