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This is a survey/ text request for noncommutative grobner basis. A googling gave me these:

http://www.sciencedirect.com/science/article/pii/0304397594902836

http://www.win.tue.nl/~amc/talks/grobner.pdf

https://www.msri.org/~de/papers/pdfs/1998-001.pdf

Although I have not looked at these in detail I wanted to know which note/book/survey an expert on the field would suggest. Thanks for any input.

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    $\begingroup$ I would prefer Arjeh M. Cohen's notes, but I am not an expert for noncommutative Gröbner bases. For more references, see here. $\endgroup$ Jul 17, 2015 at 18:29
  • $\begingroup$ I agree with Dietrich Burde, I read Cohen's notes and found them to be very accessible at an introductory level, yet giving nearly all the essential details needed to extend definitions and algorithms for standard (communtative polynomial ring) Grobner bases to non-commutative polynomial ring Grobner bases. Just note that it is not addressed whether you can actually TELL if the Grobner basis will be infinite. There may be results about this you can find elsewhere. My guess is that determining finiteness may be a (computer) undecidable problem. $\endgroup$ Jul 17, 2015 at 18:36

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