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For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

If one root of the equation f(x)=0, which is irreducible over a field K, is also a root of the equation F(x)=0 in K, then all the roots of the irreducible equation f(x)=0 are ...

Given a ring R with identity, the general linear group GL_n(R) is the group of n×n invertible matrices with elements in R. The general linear group GL_n(q) is the set of n×n ...

Perhaps the most commonly-studied oriented point lattice is the so-called north-east lattice which orients each edge of L in the direction of increasing coordinate-value. ...

Given a linear code C of length n and dimension k over the field F, a parity check matrix H of C is a n×(n-k) matrix whose rows generate the orthogonal complement of C, i.e., ...

Set covering deployment (sometimes written "set-covering deployment" and abbreviated SCDP for "set covering deployment problem") seeks an optimal stationing of troops in a ...

The term "transition matrix" is used in a number of different contexts in mathematics. In linear algebra, it is sometimes used to mean a change of coordinates matrix. In the ...

The direct product is defined for a number of classes of algebraic objects, including sets, groups, rings, and modules. In each case, the direct product of an algebraic ...

Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a region D in the plane with boundary partialD, Green's theorem states ...