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Tensor product of incidence algebras and group algebras
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 84 (2023), pp. 5-13 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $I(X, R)$ and $I(Y, S)$ be incidence algebras, where $X$ and $Y$ are preordered sets, $R$ and $S$ are algebras over some commutative ring $T$. We prove the existence of a homomorphism of algebras $I(X, R)\otimes_T I(Y, S)\to I(X\times Y, R\otimes_T S)$. If $X$ and $Y$ are finite sets, then there is an isomorphism. For arbitrary groups $G$ and $H$, it is proved that the isomorphism of algebras $R[G]\otimes_T S[H]\cong (R\otimes_T S)[G\times H]$ is valid.
Keywords: tensor product, incidence algebras, group algebra. 
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I. V. Dudin; P. A. Krylov. Tensor product of incidence algebras and group algebras. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 84 (2023), pp. 5-13. http://geodesic.mathdoc.fr/item/VTGU_2023_84_a0/

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