### Projective dimension of second order symmetric derivation of Kahler modules for hypersurfaces

#### Abstract

$R = k[x_1,...,x_s]$ be a polynomial algebra and I be an ideal of R generated by $f \in R.$ Then $S=R/I=\frac{k[x_1,...,x_s]}{(f)} $ be an affine domain which is called hypersurfaces. $\Omega_1(S)$ denotes the module of first order derivations of K\"{a}hler modules over S. $\vee^2 (\Omega_1(S))$ denotes the module of second order derivations of symmetric algebra on $\Omega_1(S).$ In this paper, we prove that if S be an affine domain represented by $ S=\frac{k[x_1,...,x_s]}{(f)}$, then projective dimension of $\vee^2(\Omega_1(S))$ is less than or equal to 1.

**Published:**2017-07-14

**How to Cite this Article:**Hamiyet Merkepci, Necati Olgun, Ela Aydin, Projective dimension of second order symmetric derivation of Kahler modules for hypersurfaces, Algebra Letters, Vol 2017 (2017), Article ID 6 Copyright © 2017 Hamiyet Merkepci, Necati Olgun, Ela Aydin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Algebra Letters

ISSN 2051-5502

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