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Comment on and a characterization of the concept of complete residuated lattice. (English) Zbl 1158.42302

Summary: We prove that some properties of the definition of complete residuated lattice can be derived from the other properties. Furthermore we prove that the concept of strictly two-sided commutative quantale and the concept of complete residuated lattice are equivalent notions.

MSC:

42A20 Convergence and absolute convergence of Fourier and trigonometric series
42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
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