title={GR{\"O}BNER BASES AND DETERMINANTAL IDEALS -- An Introduction},
  author={Winfried. Bruns},
We give an introduction to the theory of determinantal ideals and rings, their Gröbner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the Knuth-Robinson-Schensted correspondence. The article contains a section treating the basic results about the passage to initial ideals and algebras. Let K be a field and X an m × n matrix of indeterminates over K. For a given positive integer t ≤ min(m, n), we consider the ideal I t = I t (X) generated by… CONTINUE READING
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