Direct sums induce a product on M (see [13] for details).

1 and 2] give recurrences that reduce the computation of the Mobius function [mu]([sigma], [tau]) to Mobius function calculations of the form [mu]([sigma]', [tau]') where [tau]' is a single component of [tau] and [sigma]' is a

direct sum of consecutive components of [sigma].

The tangent space has the

direct sum decomposition into subbundles:

explores advanced topics in

direct sum decompositions of abelian groups and their consequences.

presents an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together

direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization.

We define their

direct sum M [

direct sum] M' on the ground set E [?

If V is a

direct sum of irreducible kG-submodules, then we call V (as well as G and [phi]) completely reducible.

q]-connection on a left U-module E, [pi] is the projection on the first summand in the

direct sum M [

direct sum] N, and [pi]([omega] [[cross product].

Although every direct summand of a [pi]-Rickart module is [pi]-Rickart, we give an example to show that a

direct sum of [pi]-Rickart modules need not be [pi]-Rickart.

Let X, Y [subset] V be two subspaces of a vector space V such that X [intersection] Y = {0}, then their

direct sum is denoted by X [

direct sum] Y.

Assume that J has a local linking at 0 with respect to a

direct sum decomposition H = [H.

We show that such a polytope is lattice equivalent to a

direct sum of del Pezzo polytopes, pseudo del Pezzo polytopes, or a (possibly skew) bipyramid over (pseudo) del Pezzo polytopes.