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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the representation of lattices by modules
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by George Hutchinson PDF
Trans. Amer. Math. Soc. 209 (1975), 311-351 Request permission

Abstract:

For a commutative ring $R$ with unit, a lattice $L$ is “representable by $R$-modules” if $L$ is embeddable in the lattice of submodules of some unitary left $R$-module. A procedure is given for generating an infinite first-order axiomatization of the class of all lattices representable by $R$-modules. Each axiom is a universal Horn formula for lattices. The procedure for generating the axioms is closely related to the ring structure, and is “effective” in the sense that many nontrivial axioms can be obtained by moderate amounts of computation.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 209 (1975), 311-351
  • MSC: Primary 06A20
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0376462-5
  • MathSciNet review: 0376462