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A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

A unit ring is a ring with a multiplicative identity. It is therefore sometimes also known as a "ring with identity." It is given by a set together with two binary operators ...

A variety is a class of algebras that is closed under homomorphisms, subalgebras, and direct products. Examples include the variety of groups, the variety of rings, the ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

The method of d'Alembert provides a solution to the one-dimensional wave equation (partial^2y)/(partialx^2)=1/(c^2)(partial^2y)/(partialt^2) (1) that models vibrations of a ...

A von Neumann regular ring is a ring R such that for all a in R, there exists a b in R satisfying a=aba (Jacobson 1989, p. 196). More formally, a ring R is regular in the ...

A number of closed-form constants can be obtained for generalized continued fractions having particularly simple partial numerators and denominators. The Ramanujan continued ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

The integer sequence defined by the recurrence P(n)=P(n-2)+P(n-3) (1) with the initial conditions P(0)=3, P(1)=0, P(2)=2. This recurrence relation is the same as that for the ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...