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June 2017 Homology of a certain associative algebra
Nobuo IIYORI, Masato SAWABE
Hokkaido Math. J. 46(2): 227-256 (June 2017). DOI: 10.14492/hokmj/1498788019

Abstract

Let $R$ be a commutative ring, and let $A$ be an associative $R$-algebra possessing an $R$-free basis $B$. In this paper, we introduce a homology $H_{n}(A,B)$ associated to a pair $(A,B)$ under suitable hypotheses. It depends on not only $A$ itself but also a choice of $B$. In order to define $H_{n}(A,B)$, we make use of a certain submodule of the $(n+1)$-fold tensor product of $A$. We develop a general theory of $H_{n}(A,B)$. Various examples of a pair $(A,B)$ and $H_{n}(A,B)$ are also provided.

Citation

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Nobuo IIYORI. Masato SAWABE. "Homology of a certain associative algebra." Hokkaido Math. J. 46 (2) 227 - 256, June 2017. https://doi.org/10.14492/hokmj/1498788019

Information

Published: June 2017
First available in Project Euclid: 30 June 2017

zbMATH: 1371.16009
MathSciNet: MR3677882
Digital Object Identifier: 10.14492/hokmj/1498788019

Subjects:
Primary: 16E40

Rights: Copyright © 2017 Hokkaido University, Department of Mathematics

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Vol.46 • No. 2 • June 2017
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