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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

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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