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# The Dimensionality of Quotient Algebras

@inproceedings{KROOKTheDO, title={The Dimensionality of Quotient Algebras}, author={CHRIS KROOK} }

Once we have found a Gröbner basis GB for an ideal I in some free algebra U , we can consider the quotient algebra Q = U/〈GB〉. It is not guaranteed that this quotient algebra will always be finite dimensional. In fact, there are many cases where the quotient algebra is infinite dimensional and has polynomial or even exponential growth. We present some functions that investigate the dimensionality of the quotient algebra.

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