Geodesic
Unique Factorization Theorems for Subalgebras of the Incidence Algebra
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 967-977

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Yocom, K. L. Unique Factorization Theorems for Subalgebras of the Incidence Algebra. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 967-977. doi: 10.4153/CJM-1972-097-9
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