Remarks on Additive Free Abelian Groups

Introductory Remarks on Additive Free Abelian Groups 

Recall that an (additive) free abelian group A is an abelian group having a basis a , . e., each element of A can be written in one, and only one, way as a linear combination of the Oi with integer coefficients. The numbers of elements in the basis oi, if finite, is called the rank of A. 

We will denote by Z the group whose elements are the lattice points of Euclidean M-space R , with the group operation being vector addition it is a free abelian group of rank , with (1,0... 0), (0,1,0. 0), (0. 0,1) as a basis. 

We will frequently use the fact that two free abelian groups are isomorphic if, and only if, they have the same rank. Recall that the proof is based on the useful facts 

W These mathematical criteria of the quality of a synthesis often relate to the overall yield, or number of steps, or cost of labor and materials that are needed to produce a unit amount of the target compound. 

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A. Introductory Remarks on Additive Free Abelian Groups... 

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