I am a bachelor scholar and I am really doing my bachelor thesis about an article of Cataneo, Felder and Tomassini, that are utilizing the work of Rozenfel’d and Bernshtein. On this final supply, they outline the area of all of the formal vector fields of rank n to be all of the linear mixture f_1(d/dx_1)+…f_n(d/dx_n), with the f_i in R[[x_1…x_n]], they usually say that it’s a Lie Algebra. But when i am not flawed, to be a Lie algebra, it must be first a vector area (by definition), and on this case, R[[x_1…x_n]] must be a area. However plainly it isn’t a area, since x_1 has no inverse factor. Can somebody please clarify to me the place I’m flawed?
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