English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we continue the investigations on the algebraic structure of afinite semigroup $S$ that is determined by its associated upper non-nilpotentgraph $\mathcal{N}_{S}$. The vertices of this graph are the elements of $S$ andtwo vertices are adjacent if they generate a semigroup that is not nilpotent(in the sense of Malcev). We introduce a class of semigroups in which theMal'cev nilpotent property lifts through ideal chains. We call this the classof \B\ semigroups. The definition is such that the global information that asemigroup is not nilpotent induces local information, i.e. some two-generatedsubsemigroups are not nilpotent. It turns out that a finite monoid (inparticular, a finite group) is \B\ if and only if it is nilpotent. Our mainresult is a description of \B\ finite semigroups $S$ in terms of theirassociated graph ${\mathcal N}_{S}$. In particular, $S$ has a largest nilpotentideal, say $K$, and $S/K$ is a 0-disjoint union of its connected components(adjoined with a zero) with at least two elements.

A description of a class of finite semigroups that are near to being Malcev nilpotent