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Global dimension of associative algebras

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 357))

Abstract

Let G be a connected graded s.f.p. (standard finitely presented) associative algebra over a field K. We show that the global dimension of G is effectively computable in the following cases: 1) G is a finitely presented monomial algebra; 2) G is a connected graded s.f.p. algebra and the associated monomial algebra A(G) has finite global dimension. The situation is considerably simpler when G has polynomial growth of degree d and gl.dim A(G)<∞. We show that in this case gl.dim G=gl.dim A(G)=d.

Partially supported by Contract No.62/1988, Committee of Science, Bulgaria.

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References

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Authors and Affiliations

  1. Institute of Mathematics, Bulgarian Academy of Sciences, P.O. Box 373, 1090, Sofia, Bulgaria

    Tatiana Gateva-Ivanova

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  1. Tatiana Gateva-Ivanova
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Teo Mora

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© 1989 Springer-Verlag Berlin Heidelberg

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Gateva-Ivanova, T. (1989). Global dimension of associative algebras. In: Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1988. Lecture Notes in Computer Science, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51083-4_61

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  • DOI: https://doi.org/10.1007/3-540-51083-4_61

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51083-3

  • Online ISBN: 978-3-540-46152-4

  • eBook Packages: Springer Book Archive

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