Some characterizations of upper semimodular lattices and posets.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1343.06001
author: R. S. Shewale
author: V. S. Kharat
publication date: 2016-04-13T00:00:00Z
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06C10
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06A11
zbMATH DE Number: 6568272
zbMATH Keywords: semimodular lattices
zbMATH Keywords: semimodular finite lattices
zbMATH Keywords: semimodular posets
zbMATH Keywords: MacLane conditions
zbMATH Keywords: M-symmetry
zbMATH Keywords: forbidden posets
MaRDI profile type: Publication
title: Some characterizations of upper semimodular lattices and posets.
published in: The Journal of the Indian Mathematical Society. New Series
review text: In the context of semimodularity in finite lattices, the authors have introduced two new conditions to describe upper semimodularity. The relationships between the new conditions and other classical ones due to Mac Lane are analyzed in depth. Then the authors furnish a generalization for posets of all these conditions previously introduced for semimodular lattices. In this direction, in order to characterize finite upper semimodular posets, the authors have discovered a forbidden structure which is studied in a section of the manuscript. Concerning all the items introduced and considered, the authors also give suitable counterexamples. A final table of implications showing the hierarchies among the concepts and conditions introduced and analyzed closes the paper.
reviewed by: Esteban Induraín
description: scientific article; zbMATH DE number 6568272