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Artinian algebras and differential forms | Guillermo Corti~nas
; Fabiana Krongold
; | Date: |
26 Dec 1999 | Journal: | Comm. in Alg. 27:4 (1999) 1711-1716 | Subject: | Algebraic Geometry; Commutative Algebra | math.AG math.AC | Affiliation: | University of Buenos Aires | Abstract: | This article concerns commutative algebras over a field $k$ of characteristic zero which are finite dimensional as vectorspaces, and particularly those of such algebras which are graded. Here the term graded is applied to non-negatively graded algebras $A$ with $A_0$ reduced and finite dimensional. Thus the trivial grading $A=A_0$ is only allowed if $A$ is a product of finite field extensions of $k$. It has been conjectured (G. Corti~nas, S. Geller, C. Weibel; The Artinian Berger Conjecture. Math. Zeitschrift {f 228} 3 (1998) 569-588) that for all finite dimensional algebras $A$ which are not principal ideal algebras (i.e. have at least one nonprincipal ideal), the following submodule of the Kähler differentials is nonzero: $$igcap{ker(Omega_A @>>>Omega_B)}$$ Here the intersection is taken over all principal ideal algebras $B$ and all homomorphisms $A @>>>B$. In this paper we prove that the conjecture holds for both Gorenstein graded and standard graded algebras. | Source: | arXiv, math.AG/0001147 | Services: | Forum | Review | PDF | Favorites |
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