Abstract.
In this paper we establish several equivalent conditions for every regular element (quasi-regular ideal) of a principally generated C-lattice L (a commutative ring with identity R) to be an invertible element of L (quasi-invertible ideal of R). Using these results, some new characterizations are given for almost Dedekind lattices, almost Dedekind rings, Dedekind lattices and Dedekind rings.
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Dedicated to George Grätzer and E. Tamás Schmidt on their 70th birthdays
Received April 10, 2006; accepted in final form April 4, 2007.
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Jayaram, C. Regular elements in multiplicative lattices. Algebra univers. 59, 73–84 (2008). https://doi.org/10.1007/s00012-008-2066-0
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DOI: https://doi.org/10.1007/s00012-008-2066-0
Keywords and phrases:
- Almost Dedekind lattice
- WI-ring
- Almost Dedekind ring
- Dedekind ring
- regular element
- quasi-regular ideal
- quasi-invertible ideal