For computing different invariants of an ideal, its position may be very important and has high effect on relevant computations. For instance, if an ideal is in an appropriate position we can compute its dimension and radical easier. So one of the important subject in algebraic geometry and computer algebra is to find a good position for a given ideal such that we can compute its invariants simply. It should be noted that, when we change the position of an ideal, many of its invarinant remain stable. One of the most important position in the polynomial ideal theory is Noether normalization or equivalently, Noether position. Noether normalization is a very important part of commutative algebra (cf. e.g. (Eisebud, 1995)). The “Noether normalization lemma” is usually proved in a constructive manner, but a computationally satisfactory solution exists. For most of the computational approaches today it is common that the application of a random change of coordinates produces very large results, which are difficult to handle afterwards. A general algorithm for the computation of a Noether normalization was outlined by Vasconcelos (Vasconcelos, 1998). The method for Noether normalization given in Section 2 of the present thesis can be understood as a specialization of this algorithm. In particular, the problem of deciding whether an ideal contains a monic polynomial in a given variable is addressed without computing the intersection of the ideal with a subring, and a way to choose a sparse coordinate change is explained. Along these lines, a (probabilistic) algorithm was presented by A. Logar in (Logar, 1989), which comes up with a relatively sparse coordinate transformation that puts a prime ideal into Noether position (and, after small modifications, a non- prime ideal as well). However, this algorithm is based on intersecting with a subring and makes use of very expensive Gr?bner basis computations w.r.t. the lexicographical term ordering. In comparison to Logar’s suggestion, the approach described in Section 4 computes Janet bases only with respect to the degree-reverse lexicographical ordering and further narrows down the set of variables which should be altered by a coordinate change. Similarly, in (Greuel and Pfister, 2008) an algorithm is described which applies a random triangular linear coordinate change and again uses the lexicographical term ordering. Examples show that the method of the present thesis in Section 4 seems to be more efficient and gives sparser results than implementations in Singular(Greuel et al., 2005). The present thesis gives guidance of how to replace the above mentioned random coordinate change by a more deterministic one. The proposed algorithm is still probabilistic, in the sense that the coefficients of the coordinate change need to be chosen outside of an algebraic hypersurface, but the number of non-zero coefficients is drastically reduced, and the obstructions for the algorithm to achieve progress are clearly identified. The last approach that we mention is that of Hashemi 2008, where coefficient growth is suggested to be counteracted by modular computations and an incremental strategy for random linear coordinate changes is proposed. However, no explicit method for determining non-zero entries in the transformation matrix is given.