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Vanishing of Hochschild Cohomologies for Local Rings with Embedding Dimension Two

Published online by Cambridge University Press:  20 November 2018

Mitsuo Hoshino
Mitsuo Hoshino*
Affiliation:
Institute of Mathematics, University of Tsukuba Ibaraki, 305 Japan
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Abstract

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Let S = k[[x,y]] be a formal power series ring in two variables x, y over a field k and I an (x, y)-primary ideal of S. We show that S/I is selfinjective if Hi(S/I, S/I ⊗k S/I) = 0 for i = 1 and 2.

Keywords

13E1016E4016L60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 59 - 65
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Asashiba, H., The selfinjectivity of a local algebra A and the condition CMS Conf. Proc. 11(1991), 9–23.Google Scholar
2. Asashiba, H. and Hoshino, M., Bilinear maps which define local algebras with trivial Hochschild cohomology, CMS Conf. Proc. 14(1993), 15–28.Google Scholar
3. Asashiba, H. and Hoshino, M., Local rings with vanishing Hochschild cohomologies, Comm. Algebra 22(1994), 2309–2316.Google Scholar
4. Auslander, M., Coherent functors, Proc. Conf. Cat. Algebra, Springer, Berlin, 1966, 189–231.Google Scholar
5. Hoshino, M., On algebras with radical cube zero, Arch. Math. 52(1989), 226–232.Google Scholar
6. Nakayama, T., On algebras with complete homology, Abh. Math. Sem. Univ. Hamburg 22(1958), 300–307.Google Scholar
7. Tachikawa, H., Quasi-Frobenius rings and generalizations, Lecture Notes in Math. 351, Springer, Berlin, 1973.Google Scholar
8. Zeng, Q., Vanishing of Hochschilds cohomologies Hi(A ⊗k A) and gradability of a local commutative algebra A, Tsukuba J. Math. 14(1990), 263–273.Google Scholar
9. Zeng, Q., On the vanishing of Hochschild cohomology Hx (A, A ®k A) for a local algebra A, Tsukuba J. Math. 16(1992), 363–376.Google Scholar
10. Zeng, Q., Vanishing of Hochschild cohomologies and directed graphs with polynomial weights, J. Algebra 154(1993), 387–405.Google Scholar