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

S. Bouchiba () and S. Kabbaj ()
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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

A chapter in Rings, Polynomials, and Modules, 2017, pp 53-77 from Springer

Abstract: 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 ) $$\mathop{\mathrm{codim}}\nolimits (R):=\mathop{ \mathrm{embdim}}\nolimits (R) -\dim (R)$$ .

Keywords: Tensor product of k-algebras; Regular ring; Embedding dimension; Krull dimension; Embedding codimension; Separable extension; 13H05; 13F20; 13B30; 13E05; 13D05; 14M05; 16E65 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-65874-2_4

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DOI: 10.1007/978-3-319-65874-2_4

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