On tensor products of matrix factorizations

Let K be a field. f∈K[[x1,...,xr]] and g∈K[[y1,...,ys]] nonzero elements. If X (resp. Y) is matrix factorization of f g), Yoshino had constructed tensor product (of factorizations) ⊗ˆ such that X⊗ˆY f+g∈K[[x1,...,xr,y1,...,ys]]. In this paper, we propose bifunctorial operation ⊗˜ its variant ⊗˜′ X⊗˜Y X⊗˜′Y are two different factorizations fg∈K[[x1,...,xr,y1,...,ys]]. We call the multiplicative Y. Several properties proved. Moreover, find three functorial variants Yoshino's ⊗ˆ. Then, (or variant) used in conjunction with any variants) to give an improved version standard algorithm for factoring polynomials using matrices on class summand-reducible defined paper. Our produces factors whose size at most one half obtains method.