invertible element

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• Invertible sheaf — In mathematics, an invertible sheaf is a coherent sheaf S on a ringed space X , for which there is an inverse T with respect to tensor product of O X modules. That is, we have : S otimes; T isomorphic to O X , which acts as identity element for… …   Wikipedia

• Inverse element — In abstract algebra, the idea of an inverse element generalises the concept of a negation, in relation to addition, and a reciprocal, in relation to multiplication. The intuition is of an element that can undo the effect of combination with… …   Wikipedia

• Non-invertible — Matrice inversible En mathématiques et plus particulièrement en algèbre linéaire, une matrice carrée A d ordre n est dite inversible ou régulière ou encore non singulière, s il existe une matrice B d ordre n telle que AB = BA = In, ( AB = In… …   Wikipédia en Français

• Banach algebra — In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space. The algebra multiplication and the Banach… …   Wikipedia

• Cancellation property — In mathematics, the notion of cancellative is a generalization of the notion of invertible. An element a in a magma (M,*) has the left cancellation property (or is left cancellative) if for all b and c in M, a * b = a * c… …   Wikipedia

• Unit (ring theory) — In mathematics, a unit in a (unital) ring R is an invertible element of R , i.e. an element u such that there is a v in R with : uv = vu = 1 R , where 1 R is the multiplicative identity element.That is, u is an invertible element of the… …   Wikipedia

• Quasitriangular Hopf algebra — In mathematics, a Hopf algebra, H, is quasitriangular[1] if there exists an invertible element, R, of such that for all , where Δ is the coproduct on H, and the linear map is …   Wikipedia

• Alternative algebra — In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have *x(xy) = (xx)y *(yx)x = y(xx)for all x and y in the algebra. Every associative algebra is… …   Wikipedia

• Division (mathematics) — Divided redirects here. For other uses, see Divided (disambiguation). For the digital implementation of mathematical division, see Division (digital). In mathematics, especially in elementary arithmetic, division (÷ …   Wikipedia

• Unit ring — In mathematics, a unit ring or ring with a unit is a unital ring, i.e. a ring R with a (multiplicative) unit element, denoted by 1 R or simply 1 if there is no risk of confusion. Alternative definitions of a ring Some authors (such as Herstein)… …   Wikipedia

• Glossary of ring theory — Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. Contents 1 Definition of a ring 2 Types of… …   Wikipedia