ar X iv : m at h / 04 11 62 2 v 1 [ m at h . R A ] 2 8 N ov 2 00 4 ALGEBRAIC AND F - INDEPENDENT SETS IN 2 - FIRS
نویسنده
چکیده
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 ∈ 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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