We study basic properties including convolutions, multiplicative functions, periodic functions, Ramanujan–Fourier series and incidence functions on posets. We co-operate with Emil Daniel Schwab (University of Texas at El Paso, USA), V. Sitaramaiah (India) and Laszlo Toth (University of Pecs, Hungary). We have shown among others that the elements of commutative Möbius monoids possess a unique factorization into product of prime elements. We have applied the Cauchy residue theorem to find the order of the usual product of rational arithmetic functions, which was left open by the famous Indian mathematician R. Vaidyanathaswamy in Trans. Amer. Math. Soc. (1931). The same applies to the usual product of linear recurrence relations and discrete-time signals. Examples of research papers are
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