On certain weighted partitions and finite semisimple rings

Authors:
L. B. Richmond and M. V. Subbarao

Journal:
Proc. Amer. Math. Soc. **64** (1977), 13-19

MSC:
Primary 10J20

MathSciNet review:
0439789

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Abstract: Let *k* be a fixed integer and define . Thus is the ordinary divisor function and is the number of *k*th powers dividing *n*. We derive the asymptotic behaviour as of defined by

*n*where we recognize different colours of the integer

*m*when it occurs as a summand in a partition. The case is of special interest since the number of semisimple rings with

*n*elements when is given by .

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1977-0439789-1

Article copyright:
© Copyright 1977
American Mathematical Society