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Weak complemented and weak invertible elements in C-lattices

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Abstract

In this paper, we prove that an indecomposable M-lattice is either a principal element domain or a special principal element lattice. Next, we introduce weak complemented elements and characterize reduced M-lattices in terms of weak complemented elements. We also study weak invertible elements and locally weak invertible elements in C-lattices and characterize reduced Prüfer lattices, WI-lattices, reduced almost principal element lattices, and reduced principal element lattices in terms of locally weak invertible elements.

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Authors and Affiliations

  1. Department of CMP, University of the West Indies, Cave Hill Campus, P.O. Box 64, Bridgetown, Barbados

    C. Jayaram

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  1. C. Jayaram
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Correspondence to C. Jayaram.

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Presented by W. McGovern.

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Jayaram, C. Weak complemented and weak invertible elements in C-lattices. Algebra Univers. 77, 237–249 (2017). https://doi.org/10.1007/s00012-017-0423-6

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  • DOI: https://doi.org/10.1007/s00012-017-0423-6

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