Abstract
Let K be a field and let f ∈ K[[x1, x2,. . . , xr]] and g ∈ K[[y1, y2, . . . , ys]] be non-zero and non-invertible elements. If X (resp. Y) is a matrix factorization of f (resp. g), then we can construct the matrix factorization X ⊗ Y of f + g over K[[x1, x2, . . . , xr, y1, y2, . . . , ys]], which we call the tensor product of X and Y. After showing several general properties of tensor products, we will prove theorems which give bounds for the number of indecomposable components in the direct decomposition of X ⊗ Y.
Original language | English |
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Pages (from-to) | 39-56 |
Number of pages | 18 |
Journal | Nagoya Mathematical Journal |
Volume | 152 |
DOIs | |
Publication status | Published - Dec 1998 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)