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Convolutions with Unbounded Unity

Published online by Cambridge University Press:  20 November 2018

V. Sitaramaiah  and
M. V. Subbarao
V. Sitaramaiah
Affiliation:
Department of Mathematics, Pondicherry Engineering College, Pillaichavday, Pondicherry—605104, India
M. V. Subbarao
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1
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Abstract

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On the set F of complex-valued arithmetic functions we construct an infinite family of convolutions, that is, binary operations ψ of the form

so that (F, +, ψ) is a commutative ring, for which the unity is unbounded. Here + denotes pointwise addition.

Keywords

11A25Arithmetic convolutionunity of a ring
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 542 - 546
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Cohen, E., Arithmetical functions associated with the unitary divisors of an integer, Math. Z. 74 (1960), 66–80.Google Scholar
2. Lehmer, D. H., Arithmetic of double series, Trans. Amer. Math. Soc. 33 (1931), 945–952.Google Scholar
3. Narkiewicz, W., On a class of arithmetical convolutions, CoWoq.Math. 10 (1963), 81–94.Google Scholar
4. Subbarao, M. V., On some arithmetic convolutions, in Theory of Arithmetic Functions. Springer Lecture Notes in Mathematics 261, Berlin, 1972, 247–271.Google Scholar