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Embedding Dimension and Codimension of Tensor Products of Algebras over a Field

In: Rings, Polynomials, and Modules

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  • S. Bouchiba

    (University of Meknes, Department of Mathematics)

  • S. Kabbaj

    (King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics)

Abstract

Let k be a field. This paper investigates the embedding dimension and codimension of Noetherian local rings arising as localizations of tensor products of k-algebras. We use results and techniques from prime spectra and dimension theory to establish an analogue of the “special chain theorem” for the embedding dimension of tensor products, with effective consequence on the transfer or defect of regularity as exhibited by the (embedding) codimension given by codim ( R ) : = embdim ( R ) − dim ( R ) $$\mathop{\mathrm{codim}}\nolimits (R):=\mathop{ \mathrm{embdim}}\nolimits (R) -\dim (R)$$ .

Suggested Citation

  • S. Bouchiba & S. Kabbaj, 2017. "Embedding Dimension and Codimension of Tensor Products of Algebras over a Field," Springer Books, in: Marco Fontana & Sophie Frisch & Sarah Glaz & Francesca Tartarone & Paolo Zanardo (ed.), Rings, Polynomials, and Modules, pages 53-77, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-65874-2_4
    DOI: 10.1007/978-3-319-65874-2_4
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