0

Each t-norm can be identified with its Cayley tomonoid, which consists of pairwise commuting order-preserving functions from the real unit interval to itself. Cayley tomonoids provide an easily manageable, yet versatile tool for the construction of t-norms. To give evidence to this claim, we review and reformulate several construction methods that are known in the literature. We adopt, on the o...

2 Linear Algebra 3 2.1 Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Vector norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Induced matrix norms. . . . . . . . . . . . . . . . . . . . . . . . ....

A (continuous) t-norm is called equationally definable when the corresponding standard BL-algebra [0, 1]∗ defined by ∗ and its residuum is the only (up to isomorphism) standard BL-algebra that generates the same variety Var([0, 1]∗). In this chapter we check that a continuous t-norm ∗ is equationally definable if and only if the t-norm is a finite ordinal sum of copies of the three basic contin...

Recall that for C-algebras A and B there are many possible norms on A ⊗ B for which the completion is a C-algebra. In particular there are two standard completions A ⊗min B and A⊗max B corresponding to the ‘smallest’ and ‘largest’ possible tensor norms. We say that A is nuclear if these two tensor products correspond for all C-algebras B. We say that a C-algebra A is exact if given any short ex...