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The hyperbolic volume of the knot complement of a hyperbolic knot is a knot invariant. Adams (1994) lists the hyperbolic volumes for knots and links. The hyperbolic volume of ...

The extension of a, an ideal in commutative ring A, in a ring B, is the ideal generated by its image f(a) under a ring homomorphism f. Explicitly, it is any finite sum of the ...

The idiosyncratic polynomial is the bivariate graph polynomial defined as the characteristic polynomial in x of A+y(J-I-A), where A is the adjacency matrix, J is the unit ...

Let sigma_infty(n) be the sum of the infinitary divisors of a number n. An infinitary perfect number is a number n such that sigma_infty(n)=2n. The first few are 6, 60, 90, ...

Let (A,<=) be a well ordered set. Then the set {a in A:a<k} for some k in A is called an initial segment of A (Rubin 1967, p. 161; Dauben 1990, pp. 196-197; Moore 1982, pp. ...

A function defined for all positive integers, sometimes also called an arithmetic function (Nagell 1951, p. 26) or number theoretic function (Wilf 1994, p. 58).

A partially ordered set P=(X,<=) is an interval order if it is isomorphic to some set of intervals on the real line ordered by left-to-right precedence. Formally, P is an ...

A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...

A nonzero module M over a ring R whose only submodules are the module itself and the zero module. It is also called a simple module, and in fact this is the name more ...

Let R[z]>0, 0<=alpha,beta<=1, and Lambda(alpha,beta,z)=sum_(r=0)^infty[lambda((r+alpha)z-ibeta)+lambda((r+1-alpha)z+ibeta)], (1) where lambda(x) = -ln(1-e^(-2pix)) (2) = ...