Geodesic
The Decomposition of the Module of n-th Order Differentials in Arbitrary Characteristic
Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 512-517

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Throughout this paper, it is assumed that A is the complete, equicharacteristic, local ring of an algebraic curve at a one-branch singularity whose residue field is algebraically closed and contained in A. Hence, the domain A is dominated by only one valuation ring in its quotient held F, and if t is a uniformizing parameter, then the integral closure of A in F, denoted by Ā, is [[t]]. 
Fischer, Klaus G. The Decomposition of the Module of n-th Order Differentials in Arbitrary Characteristic. Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 512-517. doi: 10.4153/CJM-1978-046-2
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[1] 1. Brown, W., Blow up sequences and the module of n-th order differentials, Can. J. Math. 28 (1976), 1289–1301. Google Scholar

[2] 2. Fischer, K., The module decomposition of I (A/A), Trans. Amer. Math. Soc. 186 (1973), 113–128. Google Scholar

[3] 3. Zariski, O. and Samuel, P., Commutative algebra, vol. II (D. Van Nostrand, Princeton, 1960). Google Scholar

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