exact after tensoring, a pure submodule defines a short exact sequence (known as a pure exact sequence) that remains exact after tensoring with any module...

\mathbb {Q} } is a flat Z {\displaystyle \mathbb {Z} } -module. Therefore, tensoring with Q {\displaystyle \mathbb {Q} } as a Z {\displaystyle \mathbb {Z}...

= Spin(3) (as it sits inside the 3-dimensional Clifford algebra) have tensored to produce a 4-dimensional representation. The 4-dimensional representation...

⊗ A {\displaystyle B\otimes A} , the distinction between tensoring on the left and tensoring on the right becomes immaterial, so every right closed braided...

null-vector. If ξ {\displaystyle \xi } is a CP1 projective vector, it can be tensored with its Hermitian conjugate to produce a 2 × 2 {\displaystyle 2\times...

O ( D ) {\displaystyle {\mathcal {O}}(D)} is locally free, and hence tensoring that sequence by O ( D ) {\displaystyle {\mathcal {O}}(D)} yields another...

It captures the algebraic essence of tensoring, without making any specific reference to what is being tensored. Thus, all tensor products can be expressed...

saying the manifold is complex (which is what the chart definition says). Tensoring the tangent bundle with the complex numbers we get the complexified tangent...

summands of free modules. Flat modules are defined by the property that tensoring with them preserves exact sequences. Torsion-free modules form an even...

the natural map from the tensor product C ⊗ A to B ⊗ A is injective. Tensoring an abelian group A with Q (or any divisible group) kills torsion. That...

explicitly "complexified" to couple to electromagnetism. This is done by "tensoring in" an additional factor of the complex plane C {\displaystyle \mathbb...

anomaly, but may also refer to a mixture of two different gauge groups tensored together, like the SU(2) and the U(1) of the Standard Model. The anomaly...

\mathbb {C} }^{k}} is the sheaf of germs of smooth differential k-forms tensored with C {\displaystyle \mathbb {C} } . So, we write H D ∗ ( M , Z ( q )...

Chow group of cycles on X of dimension d modulo rational equivalence, tensored with the rational numbers. In case X is defined over the complex numbers...

representation. Another (n − 1)-dimensional irreducible representation is found by tensoring with the sign representation. An exterior power Λ k V {\displaystyle \Lambda...

also be called a pseudo-volume form, due to the additional sign twist (tensoring with the sign bundle). The volume element is a pseudotensor density according...

connected topological spaces with homotopy groups and singular homology groups tensored with the rational numbers, ignoring torsion elements and simplifying certain...

f(x)\otimes g(y)\end{cases}}} The construction has a consequence that tensoring is a functor: each right R-module M determines the functor M ⊗ R − : R...

a wide variety of different characterizations. A first point is that tensoring high powers of an ample line bundle with any coherent sheaf whatsoever...

Connes determined that our space-time has a hidden discrete structure tensored to the visible four-dimensional continuous manifold. This principle, with...

by all definitions of tensor products, irrespective of the spaces being tensored: this implies that any space with a tensor product is a symmetric monoidal...

algebra becomes a matrix algebra by extending scalars (equivalently, tensoring with a field extension), i.e. for a suitable field extension K of F, A...

{\displaystyle c_{1}(L)F=F-L^{-1}\otimes F.} It is additive on G since tensoring with a line bundle is exact. One also has: c 1 ( L 1 ) c 1 ( L 2 ) = c...

Luís Antoni Santaló Sors (October 9, 1911 – November 22, 2001) was a Spanish mathematician. He graduated from the University of Madrid and he studied at...

manifold (M,ω) are naturally isomorphic to the ordinary cohomology of M, tensored by a suitable Novikov ring associated the group of covering transformations...

Mérida: Junta de Extremadura. pp. 1–4. "Tiene 26 años, 452 metros y 28 tensores". Hoy. 31 October 2010. Gilgado, Antonio (17 April 2017). "El radar del...

antiquarks. Mathematically, the representation D(p,q) may be constructed by tensoring together p copies of the standard 3-dimensional representation and q copies...

Composing these isomorphisms yields two rational vector spaces which, after tensoring with C {\displaystyle \mathbb {C} } become isomorphic. Choosing bases...

generally a complex number. This explains why the singular cohomology must be tensored to C, and from this point of view, C can be said to contain all the periods...

K_{-p-q}(X).} As in topology, the spectral sequence degenerates after tensoring with the rationals. For arbitrary schemes of finite type over a field...