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Arithmetical functions on a locally finite, locally semi-modular, local lattice. (English) Zbl 0358.06009

This paper is a continuation of a paper by the same author which appeared in [J. Reine Angew. Math. 277, 207–217 (1975; Zbl 0358.06008)]. The author considers the set \(C(\Delta)\) of chain sets of \(\Delta\) as constructed in this paper. Then he defines arithmetical functions on \(C(\Delta)\). Using these functions, the author extends some identities obtained by D. A. Smith in [Duke Math. J. 34, 617–633 (1967; Zbl 0168.26302); ibid. 36, 15–30, 353–367 (1969; Zbl 0186.02003)].

MSC:

06A06 Partial orders, general
06C05 Modular lattices, Desarguesian lattices
11A25 Arithmetic functions; related numbers; inversion formulas
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