THE DEPTH OF AN IDEAL WITH A GIVEN
... and uj K[xj , . . . , xn ]. Hence the direct sum decomposition I = δi=1 ui K[xi , . . . , xn ] arises. Let ei = deg ui for i∑ ...
... and uj K[xj , . . . , xn ]. Hence the direct sum decomposition I = δi=1 ui K[xi , . . . , xn ] arises. Let ei = deg ui for i∑ ...
Universal exponential solution of the Yang
... The equation (1) is actually an infinite set of conditions on a and b, given by taking coefficients of xn y m on both sides of (1). For example, equating the coefficients of x2 y gives the first nontrivial condition b2 a + ab2 + 2aba = ba2 + a2 b + 2bab . We are going to write a minimal list of rela ...
... The equation (1) is actually an infinite set of conditions on a and b, given by taking coefficients of xn y m on both sides of (1). For example, equating the coefficients of x2 y gives the first nontrivial condition b2 a + ab2 + 2aba = ba2 + a2 b + 2bab . We are going to write a minimal list of rela ...
8. Commutative Banach algebras In this chapter, we analyze
... (b) Homomorphisms are continuous, so N (φ) is a closed linear subspace. If x ∈ N (φ), y ∈ A, then φ(xy) = φ(x)φ(y) = 0, so xy ∈ N (φ) also, and N (φ) is an ideal. Since φ : A → C is a linear map to the one-dimensional space C, we have that codim N (φ) = 1, so N (φ) is already maximal as a subspace ( ...
... (b) Homomorphisms are continuous, so N (φ) is a closed linear subspace. If x ∈ N (φ), y ∈ A, then φ(xy) = φ(x)φ(y) = 0, so xy ∈ N (φ) also, and N (φ) is an ideal. Since φ : A → C is a linear map to the one-dimensional space C, we have that codim N (φ) = 1, so N (φ) is already maximal as a subspace ( ...
![arXiv:math/9802122v1 [math.CO] 27 Feb 1998](http://s1.studyres.com/store/data/013469206_1-76e512f42e60a4643a93990b56cee184-300x300.png)
