Tidy Noether lattices |
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Authors: | Linda Becerra |
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Institution: | (1) University of Houston-Downtown, Houston, Texas, USA |
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Abstract: | A Noether lattice satisfying the union condition on primes which is not a domain and in which every nonzero principal element is integrally closed is characterized in terms of its direct summands. It is shown that either: (1) if has no proper nonzero direct summands, then every nonzero principal element of is integrally closed if and only if is a local Noether lattice whose maximal element is principal and has square zero; or (2) if has a proper nonzero direct summand, then every nonzero principal element of is integrally closed if and only if for each minimal direct summandA of , the quotient lattice 0,A] is an integrally closed domain.Presented by R. P. Dilworth. |
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