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A module having only one element: the singleton set {*}. It is a module over any ring R with respect to the multiplication defined by a*=* (1) for every a in R, and the ...

A quantity which does not equal zero is said to be nonzero. A real nonzero number must be either positive or negative, and a complex nonzero number can have either real or ...

A differential ideal is an ideal I in the ring of smooth forms on a manifold M. That is, it is closed under addition, scalar multiplication, and wedge product with an ...

An equation of the form P(x)=0, where P(x) is a polynomial.

Given an affine variety V in the n-dimensional affine space K^n, where K is an algebraically closed field, the coordinate ring of V is the quotient ring ...

An infinite sequence of homomorphisms of modules or additive Abelian groups ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->... (1) such that, for all indices i in Z, ...

A ring defined on a singleton set {*}. The ring operations (multiplication and addition) are defined in the only possible way, *·*=*, (1) and *+*=*. (2) It follows that this ...

A square matrix A is said to be unipotent if A-I, where I is an identity matrix is a nilpotent matrix (defined by the property that A^n is the zero matrix for some positive ...

The encrypted form of a plaintext.

A Ramsey number of the form R(k,k;2).