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The notion of height is defined for proper ideals in a commutative Noetherian unit ring R. The height of a proper prime ideal P of R is the maximum of the lengths n of the ...

The radical of an ideal a in a ring R is the ideal which is the intersection of all prime ideals containing a. Note that any ideal is contained in a maximal ideal, which is ...

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 ...

A polynomial of the form f(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0 having coefficients a_i that are all integers. An integer polynomial gives integer values for all integer ...

Given a distance-regular graph G with integers b_i,c_i,i=0,...,d such that for any two vertices x,y in G at distance i=d(x,y), there are exactly c_i neighbors of y in ...

The inverse function of the Gudermannian y=gd^(-1)phi gives the vertical position y in the Mercator projection in terms of the latitude phi and may be defined for 0<=x<pi/2 ...

Since each triplet of Yff circles are congruent and pass through a single point, they obey Johnson's theorem. As a result, in each case, there is a fourth circle congruent to ...

Jung's theorem states that the generalized diameter D of a compact set X in R^n satisfies D>=Rsqrt((2(n+1))/n), where R is the circumradius of X (Danzer et al. 1963). This ...

The Koolen-Riebeek graph is a weakly regular graph on 486 vertices with parameters (nu,k,lambda,mu)=(486,45,0,(0,9)). It is distance-regular but not distance-transitive with ...

Lattice theory is the study of sets of objects known as lattices. It is an outgrowth of the study of Boolean algebras, and provides a framework for unifying the study of ...