The freeness of a group based on a distributive lattice

Authors:
P. Hill and H. Subramanian

Journal:
Proc. Amer. Math. Soc. **51** (1975), 260-262

MSC:
Primary 20K99

MathSciNet review:
0376907

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Abstract: Let be a distributive lattice and the abelian group with the following presentation. The generators of are the elements of the lattice , and the relations are where and are arbitrary elements of . It is shown that is free abelian. In particular, is torsion free. The latter statement answers affirmatively a question posed several years ago by E. Weinberg.

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0376907-6

Keywords:
Distributive lattice,
semigroup ring,
free abelian group,
idempotent generators,
pure subgroup

Article copyright:
© Copyright 1975
American Mathematical Society