Let C denote the category of Hilbert modules which are similar to contractive Hilbert modules. It is proved that if H0, H ∈ C and if H1 is similar to an isometric Hilbert module, then the sequence 0 → H0 → H → H1 → 0 splits. Thus the isometric Hilbert modules are projective in C. It follows that ExtC (K, H) = 0, whenever n > 1, for H, K ∈ C. In addition, it is proved that (Hilbert modules simil...

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.

A partial lattice P is ideal-projective, with respect to a class C of lattices, if for every K ∈ C and every homomorphism φ of partial lattices from P to the ideal lattice of K, there are arbitrarily large choice functions f : P → K for φ that are also homomorphisms of partial lattices. This extends the traditional concept of (sharp) transferability of a lattice with respect to C. We prove the ...

For a tuple A = (A0, A1, ..., An) of elements in a unital Banach algebra B, its projective spectrum p(A) is defined to be the collection of z = [z0, z1, ..., zn] ∈ P such that A(z) = z0A0 + z1A1 + · · · + znAn is not invertible in B. The pre-image of p(A) in Cn+1 is denoted by P (A). When B is the k × k matrix algebra Mk(C), the projective spectrum is a projective hypersurface. In infinite dime...

In this paper we show that C-k(X), the set of continuous, realvalued functions on X topologized by the pointwise convergence topology, can have arbitrarily high Borel or projective complexity in Rx even when X is a countable regular space with a unique limit point. In addition we show how to construct countable regular spaces X for which C-n(X) lies nowhere in the projective hierarchy of the co...

Let R be a ring with identity and C(R) denote the category of complexes of R-modules. In this paper we study the homotopy categories arising from projective (resp. injective) complexes as well as Gorenstein projective (resp. Gorenstein injective) modules. We show that the homotopy category of projective complexes over R, denoted K(Prj C(R)), is always well generated and is compactly generated p...

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...

Let C be a smooth projective curve of genus g ≥ 2 and L be a line bundle on C of degree d. Assume that r ≥ 2 is an integer coprime with d. Let M := UC(r,L) be the moduli space of stable vector bundles on C of rank r and with the fixed determinant L. It is well-known that M is a smooth projective Fano variety with Picard number 1. For any projective curve in M , we can define its degree with res...

Introduction Let K be a number field, ax the ring of integers of K. Suppose we are given a projective curve 2, and a morphism 4 : Z 4 Pf(C) (where Pf(C) is the projective line) such that 4 and Z are both defined over K. We denote by K(Z) the field of functions of Z defined over K, and from this data we obtain a permutation representation T of the Galois group G(K(Z) "/K(Pt(C))) (where K(Z) A is...

This paper constitutes a preliminary discussion of joint work in progress as presented by the first author at Stony Brook in June 1991 at the symposium in honor of John Milnor. Our results include a construction of an intersection pairing on spaces of algebraic cycles on a given smooth complex quasi-projective variety, thereby providing a ring structure in “Lawson homology.” We verify that the ...