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Algebraic and F-Independent sets in 2-firs

A. Leroy·A. Ozturk
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Abstract

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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A. Leroy, A. Ozturk. 2004-11-28. Algebraic and F-Independent sets in 2-firs. https://arxiv.org/abs/math/0411622

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