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A regular local ring is a local ring R with maximal ideal m so that m can be generated with exactly d elements where d is the Krull dimension of the ring R. Equivalently, R ...

If pi on V and pi^' on V^' are irreducible representations and E:V|->V^' is a linear map such that pi^'(g)E=Epi(g) for all g in and group G, then E=0 or E is invertible. ...

A topological algebra is a pair (A,tau), where A=(A,(f_i^A)_(i in I)) is an algebra and each of the operations f_i^A is continuous in the product topology. Examples of ...

The vector triple product identity is also known as the BAC-CAB identity, and can be written in the form Ax(BxC) = B(A·C)-C(A·B) (1) (AxB)xC = -Cx(AxB) (2) = -A(B·C)+B(A·C). ...

The envelope of the lines connecting corresponding points on the Jacobian curve and Steinerian curve. The Cayleyian curve of a net of curves of order n has the same curve ...

The 10_3 configuration of ten lines intersecting three at a time in 10 points which arises in Desargues' theorem. Its Levi graph is the Desargues graph.

The first Morley center is the center of Morley's circle. It has triangle center function alpha_(356)=cos(1/3A)+2cos(1/3B)cos(1/3C) and is Kimberling center X_(356).

Externally erect a square on the side BC. Now join the new vertices S_(AB) and S_AC of this square with the vertex A, marking the points of intersection Q_(A,BC) and ...

In the above figure, the sides a and b have the same length, appearances to the contrary. In the related illusion illustrated above, the interior lines appear to be of ...

A perspective collineation with center O and axis o is a collineation which leaves all lines through O and points of o invariant. Every perspective collineation is a ...