This paper is concerned with factor left prime factorization problems for multivariate polynomial matrices without full row rank. We propose a necessary and sufficient condition for the existence of factor left prime factorizations of a class of multivariate polynomial matrices, and then design an algorithm to compute all factor left prime factorizations if they exist. We implement the algorithm on the computer algebra system Maple, and two examples are given to illustrate the effectiveness of the algorithm. The results presented in this paper are also true for the existence of factor right prime factorizations of multivariate polynomial matrices without full column rank.

中文翻译：

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关于多元多项式矩阵的因子左素因数分解问题

本文主要研究无满行秩的多元多项式矩阵的因子左素因数分解问题。我们提出了一类多元多项式矩阵的因子左素数分解存在的充要条件，然后设计了一种算法来计算所有因子左素数分解（如果它们存在）。我们在计算机代数系统 Maple 上实现了该算法，并给出了两个例子来说明该算法的有效性。本文中给出的结果也适用于没有满列秩的多元多项式矩阵的因子右素因数分解的存在。