For C-algebras A1, A2 the map (I1, I2) → ker(qI1 ⊗ qI2) from Id′(A1) × Id ′(A2) into Id ′(A1 ⊗min A2) is a homeomorphism onto its image which is dense in the range. Here, for a C-algebra A, the space of all proper closed two sided ideals endowed with an adequate topology is denoted Id(A) and qI is the quotient map of A onto A/I. New proofs of the equivalence of the property (F) of Tomiyama for ...

This is the second in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology QHG(X) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohomology QH(X//G) of its geometric invariant theory quotient X//G, and prove that it intertwines the genus zero gau...

We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties. For a given toric variety X we first construct a toric quasi–projective reduction. Then ...

It is proved that if a Banach space Y is a quotient of a Banach space having a shrinking unconditional basis, then every normalized weakly null sequence in Y has an unconditional subsequence. The proof yields the corollary that every quotient of Schreier's space is c o-saturated. §0. Introduction. We shall say that a Banach space Y has property (WU) if every normalized weakly null sequence in Y...

We study a basic algorithmic problem in algebraic geometry, which we call NNL, of constructing a normalizing map as per Noether’s Normalization Lemma. For general explicit varieties, as formally defined in this paper, we give a randomized polynomial-time Monte Carlo algorithm for this problem. For some interesting cases of explicit varieties, we give deterministic quasi-polynomial time algorith...

Let M be a compact Kähler manifold equipped with a Hamiltonian action of a compact Lie group G. In this paper, we study the geometric quantization of the symplectic quotient M/G. Guillemin and Sternberg [Invent. Math. 67 (1982), 515–538] have shown, under suitable regularity assumptions, that there is a natural invertible map between the quantum Hilbert space over M/G and the G-invariant subspa...

Let M be a compact Kähler manifold equipped with a Hamiltonian action of a compact Lie group G. In this paper, we study the geometric quantization of the symplectic quotient M/G. Guillemin and Sternberg [Invent. Math. 67 (1982), 515–538] have shown, under suitable regularity assumptions, that there is a natural invertible map between the quantum Hilbert space over M/G and the G-invariant subspa...

We study a basic algorithmic problem in algebraic geometry, which we call NNL, of constructing a normalizing map as per Noether’s Normalization Lemma. For general explicit varieties, as formally defined in this paper, we give a randomized polynomial-time Monte Carlo algorithm for this problem. For some interesting cases of explicit varieties, we give deterministic quasi-polynomial time algorith...

In this paper, our aim was making a metric space on hoop algebras, because of that, we introduced the notion valuation maps from F-quasi-valuation map based hoops and related properties them are investigated. By using these notions, quasi-metric space. The continuity operations is studied with topology induced by quasi-valuation. Also, homomorphism investigated that under which condition an map...