Historical background to Gröbner's paper
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In his 1965 Ph.D. thesis [2], Bruno Buchberger invented the algebraic object known today as a Gröbner basis. The thesis problem that Buchberger was given by his advisor, Wolfgang Gröbner, was that of finding a basis of the residue class ring of a zero-dimensional polynomial ideal. It is clear that Gröbner knew generally of a method for computing this [1], and indeed the last paragraph of Gröbner’s 1950 paper [3] reads (in translation)
[1] Bruno Buchberger,et al. Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal , 2006, J. Symb. Comput..
[2] Bruno Buchberger. Comments on the translation of my PhD thesis , 2006, J. Symb. Comput..
[3] Wolfgang Gröbner. On elimination theory , 1998, SIGS.