Search results for "Poset"

Relatively Orthocomplemented Skew Nearlattices in Rickart Rings

2015

AbstractA class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular.The order ≤ is actually a version of the so called right-star order. The one-sided star orders are well-investigated for matrices and recently have been generalized to bounded linear Hilbert space operators and to abstract Ric…

Posets That Locally Resemble Distributive Lattices

2000

Abstract Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a corollary, a theorem of Stanley for Boolean lattices is obtained, as well as a theorem of Grabiner (conjectured by Stanley) for products of chains. Applications to incidence geometry and connections with the theory of buildings are discussed.

Completion of partially ordered sets

2007

Measuring consumers’ level of satisfaction for online food shopping during COVID-19 in Italy using POSETs

2021

Abstract The pandemic COVID 19 has upset the economic, social, financial, and general behavioral systems. Global crisis has a large impact overall and related fallouts significantly affect existent structural paradigms in every country and region across the world. In particular, the spread of COVID-19 pandemic has led to having to rethink the way we produce and consume food. Within this global change, a rise in the number of consumers who purchase food products online in order to comply with the rules aimed at limiting the circulation of the virus should be emphasized. Consequently, probably causing a long-term positive effect on m-commerce. The purpose is to elaborate on the index of the s…