a module m is called epi-retractable if every submodule of m is a homomorphic image of m. dually, a module m is called co-epi-retractable if it contains a copy of each of its factor modules. in special case, a ring r is called co-pli (resp. co-pri) if rr (resp. rr) is co-epi-retractable. it is proved that if r is a left principal right duo ring, then every left ideal of r is an epi-retractable ...

In this paper we study the structure of the graded ring of pro-jective invariants of n ordered points on the projective line CP 1. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of rel...

The Hodge equations for 1-forms are studied on Beltrami’s projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for weakly harmonic 1-fields, changing type on the unit circle, is derived under Dirichlet conditions imposed on the non-characteristic portion of the boundary. A sim...

Star configurations are certain unions of linear subspaces of projective space. They have appeared in several different contexts: the study of extremal Hilbert functions for fat point schemes in the plane; the study of secant varieties of some classical algebraic varieties; the study of the resurgence of projective schemes. In this paper we study some algebraic properties of the ideals defining...

Suppose X is a nonsingular projective scheme, Z a nonsingular closed sub-scheme of X. Let˜X be the blowup of X centered at Z, E0 the pull-back of a general hyperplane in X, and E the exceptional divisor. In this paper, we study projective em-beddings of˜X given by divisors De,t = tE0 − eE. When X satisfies a necessary condition, we give explicit values of d and δ such that for all e > 0 and t >...

Let An(K) be the Kostant form of U(sl + n ) and Γ the monoid generated by the positive roots of sln. For each λ ∈ Λ(n, r) we construct a functor Fλ from the category of finitely generated Γ-graded An(K)-modules to the category of finite-dimensional S(n, r)-modules, with the property that Fλ maps (minimal) projective resolutions of the one-dimensional An(K)module KA to (minimal) projective resol...

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.

Imagery is often used to accomplish some computational task. In such cases there are some aspects of the imagery that are relevant to the task and other aspects that are not. In order to quantify the task-specific quality of such imagery, we introduce the concept of task-specific information (TSI). A formal framework for the computation of TSI is described and is applied to three common tasks: ...

An ideal controlled-NOT gate followed by projective measurements can be used to identify specific Bell states of its two input qubits. When the input qubits are each members of independent Bell states, these projective measurements can be used to swap the post-selected entanglement onto the remaining two qubits. Here we apply this strategy to produce heralded two-photon polarization entanglemen...

The object of this paper is to study the relationship between certain projective modules and their endomorphism rings. Specifically, the basic problem is to describe the projective modules whose endomorphism rings are (von Neumann) regular, local semiperfect, or left perfect. Call a projective module regular if every cyclic submodule is a direct summand. Thus a ring is a regular module if it is...