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Can anyone tell me where I may find an introduction to linear resolutions (of a $k[x_1,\ldots,x_n]$-module or ideal) including, of course, the standard definition of such a resolution, as well as its basic properties?

Thanks in advance.

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    Here is a simple and short lecture note by Tom Marley. https://www.math.unl.edu/~tmarley1/905notes.pdf2016-10-06

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