代数与2-fir中的F-独立集
Algebraic and F-Independent sets in 2-firs
摘要：
令$R$表示2-fir。定义了R的F-独立性和代数子集的概念。将代数子集分解为相似类给出了一种简单的方法，将F-独立性转化为某些向量空间的维数。特别地，每个元素$a \in R$附加有一定的原子代数集，并且上述分解给出了$a$的原子分解的长度的下界，该下界是根据某些向量空间的维度。引入了秩的概念，并详细研究了完全可约元。
英文摘要：
Let $R$ denote a 2-fir. The notions of F-independence and algebraic subsets of R are defined. The decomposition of an algebraic subset into similarity classes gives a simple way of translating the F-independence in terms of dimension of some vector spaces. In particular to each element $a \in R$ is attached a certain algebraic set of atoms and the above decomposition gives a lower bound of the length of the atomic decompositions of $a$ in terms of dimensions of certain vector spaces. A notion of rank is introduced and fully reducible elements are studied in details.
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