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An element admitting a multiplicative or additive inverse. In most cases, the choice between these two options is clear from the context, as, for example, in a monoid, where ...

An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

Let A be a C^*-algebra, then an element u in A is called a partial isometry if uu^*u=u.

The area element for a surface with first fundamental form ds^2=Edu^2+2Fdudv+Gdv^2 is dA=sqrt(EG-F^2)du ^ dv, where du ^ dv is the wedge product.

Given a field F and an extension field K superset= F, an element alpha in K is called algebraic over F if it is a root of some nonzero polynomial with coefficients in F. ...

A volume element is the differential element dV whose volume integral over some range in a given coordinate system gives the volume of a solid, V=intintint_(G)dxdydz. (1) In ...

Also known as the first fundamental form, ds^2=g_(ab)dx^adx^b. In the principal axis frame for three dimensions, ds^2=g_(11)(dx^1)^2+g_(22)(dx^2)^2+g_(33)(dx^3)^2. At ...

The order of the polynomial defining an algebraic curve.

The number of nodes in a graph is called its order.

A relation < is a strict order on a set S if it is 1. Irreflexive: a<a does not hold for any a in S. 2. Asymmetric: if a<b, then b<a does not hold. 3. Transitive: a<b and b<c ...