Abstract
In this paper, we characterize pseudocomplemented lattices with (ACC) and (DCC) by using their sublattices. Specifically speaking, we give a necessary and sufficient condition that a lattice with (ACC) and (DCC) is pseudocomplemented by using its nine sublattices. Moreover, we describe the interval pseudocomplementedness of semimodular lattices with (ACC) and (DCC) by their sublattices equivalently.
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The authors are grateful to the responsible editor and the anonymous referee for their valuable comments and suggestions, which helps the authors to improve the earlier version of this paper.
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Presented by G. Czédli.
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The research of the first author was supported by the National Natural Science Foundation of China No. 11901064. The research of the second author was supported by the National Natural Science Foundation of China No. 12071325.
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He, P., Wang, Xp. Characterizations of pseudocomplemented lattices by excluded 0-sublattices. Algebra Univers. 82, 29 (2021). https://doi.org/10.1007/s00012-021-00725-6
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DOI: https://doi.org/10.1007/s00012-021-00725-6