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Unique Factorization Theorems for Subalgebras of the Incidence Algebra

Published online by Cambridge University Press:  20 November 2018

K. L. Yocom
K. L. Yocom*
Affiliation:
South Dakota State University, Brookings, South Dakota
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H. Scheid [4] has found necessary and sufficient conditions on a partially ordered set S(≦) which is a direct sum of a countable number of trees for a certain subalgebra G(+, *) of the incidence algebra F(+, *) to be an integral domain. In this paper we prove that under similar conditions on S, G(+, *) is actually a unique factorization domain or, failing this, that there is a subalgebra H(+, *) of F(+, *) which is a unique factorization domain and contains G. Similar results are then obtained as corollaries in the regular convolution rings of Narkiewicz.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 5 , October 1972 , pp. 967 - 977
Copyright
Copyright © Canadian Mathematical Society 1972

References

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