Vered Moskowicz

6 Questions 4 Answers 0 Followers

Questions related from Vered Moskowicz

If (u,v) is a maximal ideal of C[x,y], then there exists an automorphism g of C[x,y] s.t. u=g(x) and v=g(y)?

Let u,v in C[x,y] and assume that (u,v) is a maximal ideal of C[x,y]. Question: Is it true that there exists an automorphism g of C[x,y] s.t. u=g(x), v=g(y)? Recall that if I is a maximal ideal...

10 September 2023 9,797 0 View

Are 'special' two-variable polynomials u and v must be symmetric polynomials?

Let u,v be polynomials in two variables x and y over the field C of complex numbers. Assume that the following 6 conditions are satisfied for all f(x) in C[x], g(y) in C[y]; the notation is of...

09 September 2023 478 2 View

For which polynomial h, C[x] is separable over k+(h)?

Let h belong to C[x] (C = complex numbers). Denote by R_h the C-subalgebra of C[x] of the form C+(h), where (h) is the ideal of C[x] generated by h. Claim: C[x] is separable over R_h iff h is...

25 January 2021 6,000 1 View

When k[x,y] is flat over a certain subring?

Let k be a field of characteristic zero and let a,b,c,d belong to k[x,y]. Assume that k[x,y] is flat over R_1=k[a+c,b+d] and over R_2=k[a-c,b-d]. Is it true that k[x,y] is flat over R=k[a,b,d,c]?...

21 December 2020 6,454 2 View

What is the form of an ideal of k[x,y] invariant under the involution (x,y)->(x,-y)?

Let k be a field of characteristic zero. Let p,q be two nonconstant polynomials in k[x,y], I the ideal generated by p and q and d an involution on k[x,y], namely, a k-algebra automorphism of...

26 May 2020 4,217 0 View

An automorphism from C(x,y) to a subfield of an algebraic closure of C(x,y)

Let R=C(u,v) be a subfield of C(x,y) with u,v in C[x,y] algebraically independent over C, with u not a square in R. Take L=R(s), where s^2=u, so [L:R]=2. Clearly, L is a subfield of an...

01 January 1970 1,189 0 View