Abstract
Lower (or: dually) semimodular lattices behave in certain situations like consistent upper semimodular lattices. A common property of both classes of lattices is that they are hereditarily strong in the sense that every interval is a strong sublattice (cf. Section 2). We relate the properties “hereditarily strong” and “consistent” as well as their duals to lower semimodularity and to modularity (Section 3). Finally we characterize modularity for consistent lower semimodular lattices by means of forbidden sublattices (Section 4).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
More From: Rendiconti del Seminario Matematico e Fisico di Milano
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
