Abstract
This paper deals with triangular norms and conorms defined on the extended set N of natural numbers ordered by divisibility. From the fundamental theorem of arithmetic, N can be identified with a lattice of functions from the set of primes to the complete chain {0, 1, 2, …, +∞}, thus our knowledge about (divisible) t-norms on this chain can be applied to the study of t-norms on N. A characterization of those t-norms on N which are a direct product of t-norms on {0, 1, 2, …, +∞} is given and, after introducing the concept of T-prime (prime with respect to a t-norm T), a theorem about the existence of a T-prime decomposition is obtained. This result generalizes the fundamental theorem of arithmetic.
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