Sentence examples for free modules from inspiring English sources

We show that B may be decomposed into a finite sum of free modules.

The problem is reduced to analyzing how the weights of a torus propagate along an equivariant map of free modules.

We explain how to determine the action of the torus on the free modules in the resolution, when the resolution can be calculated explicitly.

(1) By definition, if an algebra ({mathcal A}) does not have the IBN property, then there are m, n with (1le m <n) such that ({mathcal A}^m cong {mathcal A}^n), and this isomorphism of free modules will be implemented by matrices (X'in M_{mtimes n}({mathcal A})) and (Y' in M_{ntimes m} ({mathcal A})) such that (X'Y'=I_m) and (Y'X'= I_n).

Currently there are over 110,000 and counting free modules in the npm respository.

The algebro-geometric interpretation of commutative rings via their spectrum allows the development of concepts such as locally free modules, the algebraic counterpart to vector bundles.

The CD-lemma for modules is the CD-lemma for the doubly free module Mod k ⟨ Y ⟩ ( X ), a free module over a free associative algebra.

R is a free module over L with finite rank, and.

Q L (a) is a free module over L with rank 4.

The classification is then made easier by the fact that, in the above range for m, R is a P.I.D., hence every torsion free module is free.

In this paper, we say that a L-algebra R is a non-commutative ring only if. 1. R is a free module over L with finite rank, and   2.