In the branch of abstract mathematics called category theory, a projective cover of an object X is in a sense the best approximation of X by a projective object P. Projective covers are the dual of injective envelopes.
category theory, a projectivecover of an object X is in a sense the best approximation of X by a projective object P. Projectivecovers are the dual of...
the property of lifting that carries over from free to projective modules: a module P is projective if and only if for every surjective module homomorphism...
especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action...
identified. RP1 is called the real projective line, which is topologically equivalent to a circle. RP2 is called the real projective plane. This space cannot be...
a projectivecover, and the flat left R-modules coincide with the projective left modules. An analogue of the Baer's criterion holds for projective modules...
In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space P n {\displaystyle \mathbb {P}...
mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group P...
minimal projective resolutions, where each map is required to be a projectivecover of the kernel of the map to the right. However, projectivecovers need...
common construction of the real projective plane is as the space of lines in R3 passing through the origin. The real projective plane is then an extension...
complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space...
In geometry, a real projective line is a projective line over the real numbers. It is an extension of the usual concept of a line that has been historically...
In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations...
flat cover that is unique up to (non-unique) isomorphism. Flat covers are in some sense dual to injective hulls, and are related to projectivecovers and...
resultant elimination of special cases; for example, two distinct projective lines in a projective plane meet in exactly one point (there is no "parallel" case)...
isometry group of complex projective space, just as the projective orthogonal group is the isometry group of real projective space. In terms of matrices...
is an indecomposable, projective, cyclic module. Principal indecomposable modules are also called PIMs for short. The projective indecomposable modules...
projective-planar graphs may not itself be projective-planar but will still have a planar cover, the disjoint union of the orientable double covers....
fundamental geometric statement on projective spaces: the Euler sequence. The negativity of the canonical line bundle makes projective spaces prime examples of...
In mathematics, a projective bundle is a fiber bundle whose fibers are projective spaces. By definition, a scheme X over a Noetherian scheme S is a Pn-bundle...
Fleischer (1968). The dual notion of a projectivecover does not always exist for a module, however a flat cover exists for every module. In some cases...
equal to 1 is simple for all odd n > 1, when it is isomorphic to the projective special linear group. The first classification of simple Lie groups was...
Look up projective in Wiktionary, the free dictionary. Projective may refer to Projective geometry Projective space Projective plane Projective variety...
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