The relation type of affine algebras and algebraic varieties
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We introduce the notion of relation type of an affine algebra and prove that it is well defined by using the Jacobi-Zariski exact sequence of Andre-Quillen homology. In particular, the relation type,is an invariant of an affine algebraic variety. Also as a consequence of the invariance, we show that in order to calculate the relation type of an ideal in a polynomial ring one can reduce the problem to trinomial ideals. When the relation type is at least two, the extreme equidimensional components play no role. This leads to the non-existence of affine algebras of embedding dimension three and relation type two. (C) 2015 Elsevier Inc. All rights reserved.
CitationPlanas-Vilanova, F. A. The relation type of affine algebras and algebraic varieties. "Journal of algebra", 01 Novembre 2015, vol. 441, p. 166-179.