Sets of regular systems of divisors of a generalized integer
Abstract
The notion of a regular system of divisors of a number underlying a Narkiewicz's idea of the generalization of the familiar Dirichlet and unitary convolution of arithmetical functions is used to extend some combinatorial results about systems of subsets of divisors of a generalized integer.
Keywords
generalized integer; arithmetical semigroup; Narkiewicz's regular system of divisors
References
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3. J. Knopfmacher, Abstract Analytic Number Theory, North-Holland Mathematical Library, Vol. 12, North-Holland & American Elsevier, Amsterdam-Oxford-New York 1975; corr. and enlarged ed. Dover Publications, Inc., New York (1990).
4. W. Narkiewicz, On a class of arithmetical convolutions, Coll. Math., 10 (1963), 81-94.
5. V.S. Ramaiah, Arithmetical sums in regular convolutions, J. reine angew. Math., 303/304 (1978), 265-283.
Department of Mathematics, Institute of Chemical Technology, Czech Republic Czechia
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