Search Results for ""

A fraction containing each of the digits 1 through 9 is called a pandigital fraction. The following table gives the number of pandigital fractions which represent simple unit ...

For every ring containing p spheres, there exists a ring of q spheres, each touching each of the p spheres, where 1/p+1/q=1/2, (1) which can also be written (p-2)(q-2)=4. (2) ...

The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

The natural projection, also called the homomorphism, is a logical way of mapping an algebraic structure onto its quotient structures. The natural projection pi is defined ...

Let A be a commutative ring, let C_r be an R-module for r=0, 1, 2, ..., and define a chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0. ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...

Eisenstein's irreducibility criterion is a sufficient condition assuring that an integer polynomial p(x) is irreducible in the polynomial ring Q[x]. The polynomial ...

A fractional ideal is a generalization of an ideal in a ring R. Instead, a fractional ideal is contained in the number field F, but has the property that there is an element ...

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 ...

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 ...