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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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 $ L$ be a distributive lattice and $ G$ the abelian group with the following presentation. The generators of $ G$ are the elements of the lattice $ L$, and the relations are $ (a \vee b) + (a \wedge b) = a + b$ where $ a$ and $ b$ are arbitrary elements of $ L$. It is shown that $ G$ is free abelian. In particular, $ G$ is torsion free. The latter statement answers affirmatively a question posed several years ago by E. Weinberg.

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Keywords: Distributive lattice, semigroup ring, free abelian group, idempotent generators, pure subgroup
Article copyright: © Copyright 1975 American Mathematical Society

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