In this paper we consider the derivations for even part of the finitedimensional Hamiltonian superalgebra H over a field of prime characteristic. We first introduce an ideal N of H 0 and show that the derivation space from H 0 into W 0 can be obtained by the derivation space from N into W 0 , the even part of the generalized Witt superalgebra W . For further application we also give the generat...

|f1(z)| + |f2(z)| ≥ |f(z)| ∀z ∈ D, and such, that f2 does not belong to the ideal I generated by f1, f2, i. e. f2 cannot be represented as f2 ≡ f1g1 + f2g2, g1, g2 ∈ H∞. This gives a negative answer to an old question by T. Wolff. Note, that it was well known before that under the same assumptions f belongs to the ideal if p > 2, but a counterexample can be constructed for p < 2, so our case p ...

The duality theorem of Greenlees and May relating local cohomology with support on an ideal I and the left derived functors of I-adic completion [GM92] holds for rather general ideals in commutative rings. Here, simple formulas are provided for both local cohomology and derived functors of Z-graded completion, when I is a monomial ideal in the Z-graded polynomial ring k[x1, . . . , xn]. Greenle...

Let O be the ring of integers of a totally real number field E and set G := ResE/Q(GL2). Fix an ideal c ⊂ O. For each ideal m ⊂ O let T (m) denote the mth Hecke operator associated to the standard compact open subgroup U0(c) of G(Af ). Setting X0(c) := G(Q)\G(A)/K∞U0(c), where K∞ is a certain subgroup of G(R), we use T (m) to define a Hecke cycle Z(m) ∈ IH2[E:Q](X0(c)×X0(c)). Here IH• denotes i...

The circuit ideal, ICA , of a configuration A = {a1, . . . ,an} ⊂ Z d is the ideal generated by the binomials x + − x − ∈ k[x1, . . . , xn] as c = c − c ∈ Z varies over the circuits of A. This ideal is contained in the toric ideal, IA, of A which has numerous applications and is nontrivial to compute. Since circuits can be computed using linear algebra and the two ideals often coincide, it is w...

Let A be a local ring with 2 invertible. It is known that the localization of the cohomology ring H∗ ét(A,Z/2) with respect to the class (−1) ∈ H1 ét(A,Z/2) is isomorphic to the ring C(sperA,Z/2) of continuous Z/2-valued functions on the real spectrum of A. Let In(A) denote the powers of the fundamental ideal in the Witt ring of symmetric bilinear forms over A. The starting point of this articl...

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

We determine all nonquadratic imaginary cyclic number fields K of 2-power degrees with ideal class groups of exponents < 2, i.e., with ideal class groups such that the square of each ideal class is the principal class, i.e., such that the ideal class groups are isomorphic to some (Z/2Z)m , m > 0. There are 38 such number fields: 33 of them are quartic ones (see Theorem 13), 4 of them are octic ...

The aim of this paper is to settle a question about the tight closure of Ž 2 2 2 . w x Ž 3 3 3. the ideal x , y , z in the ring R s K X, Y, Z r X q Y q Z where Ž K is a field of prime characteristic p / 3. Lower case letters denote the . images of the corresponding variables. M. McDermott has studied the tight closure of various irreducible ideals in R and has established that Ž 2 2 2 . w x xyz...

Gu map-1 is a modified version of GGH map. It uses same ideal lattices for constructing the trapdoors, while the novelty is that no encodings of zero are given. In this short paper we show that Gu map-1 cannot be used for the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. That is, if Gu map-1 is used for such instance, we can break it by soving a combined 3-...