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Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

A generalization of the helicoid to the parametric equations x(u,v) = avcosu (1) y(u,v) = bvsinu (2) z(u,v) = cu. (3) In this parametrization, the surface has first ...

An algebraic ring which appears in treatments of duality in algebraic geometry. Let A be a local Artinian ring with m subset A its maximal ideal. Then A is a Gorenstein ring ...

The Heisenberg group H^n in n complex variables is the group of all (z,t) with z in C^n and t in R having multiplication (w,t)(z,t^')=(w+z,t+t^'+I[w^*z]) (1) where w^* is the ...

The Heronian mean of two numbers a and b is defined as HM(a,b) = 1/3(2A+G) (1) = 1/3(a+sqrt(ab)+b), (2) where A is the arithmetic mean and G the geometric mean. It arises in ...

Let K be an algebraically closed field and let I be an ideal in K(x), where x=(x_1,x_2,...,x_n) is a finite set of indeterminates. Let p in K(x) be such that for any ...

The ideal quotient (a:b) is an analog of division for ideals in a commutative ring R, (a:b)={x in R:xb subset a}. The ideal quotient is always another ideal. However, this ...

A branch of topology dealing with topological invariants of manifolds.

A special ideal in a commutative ring R. The Jacobson radical is the intersection of the maximal ideals in R. It could be the zero ideal, as in the case of the integers.