About Gröbner Bases

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Recently I have come across a book of Gröbner Bases written by Adams & Loustaunau. The book is excellent and I have become interested in Gröbner bases after reading the book. I want to read more on this subject. Can you recommend me any book? Also tell me about recent research activities of the scholars in this area. What are their targets which are yet to be achieved.

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  • "Ideals, Varieties, and Algorithms" by David Cox, John Little, Donal O’Shea . This book introduce Gröbner Bases and use it in various cases, for example in "Elimination Theory".
  • "Commutative Algebra" by Eisenbud (chapter 15)
  • "Monomial Ideals" by Herzog-Hibi

For recent research activities search arxiv. See also here