Computational ideal theory and groebner basis - Zheng, Jia Li (Nanyang Technological University, 2021)
For every ideal in a polynomial ring over a field, there exists a finite basis as stated by Hilbert's Basis Theorem. However, as classical proofs of the theorem are nonconstructive, several academics have attempted to develop constructive proofs of the theorem. Amongst them, Buchberger developed the theory of Groebner basis and came up with an algorithm to construct a basis from any finite generating set. In the first four sections of this paper, I shall attempt to provide an elementary introduction to the theory of Groebner basis.