31. For Gr�bner bases, a further condition must be satisfied, namely that every non constant monomial is greater than the monomial . 32. In particular, the property of " being " a Gr�bner basis is always relative to a specific monomial order. 33. The defining property of monomial orderings implies that the order of the terms is kept when multiplying a polynomial by a monomial. 34. The defining property of monomial orderings implies that the order of the terms is kept when multiplying a polynomial by a monomial . 35. Let the coefficient of this term be, then is either zero or a symmetric polynomial with a strictly smaller leading monomial . 36. If the Galois group is supersolvable or more generally monomial then all representations are of this form so the Artin conjecture holds. 37. This is for instance the case when considering a monomial basis of a polynomial ring, or a monomial ordering of that basis. 38. This is for instance the case when considering a monomial basis of a polynomial ring, or a monomial ordering of that basis. 39. His work on Geometric Invariant Theory and on Schubert varieties, in particular his introduction of standard monomial theory, is widely recognized. 40. Finding invariants for a given subgroup of is relatively easy; one can sum the orbit of a monomial under the action of.
