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

PROOF. If R satisfies (C) then, for each nonzero element a in R the equations ax = c and xa = c have solutions x in R, and so R is a division ring as is shown in many places. (For example, see page 87 of [7].) In view of this lemma our question reduces to QUESTION 1. Can a noncommutative division ring satisfy condition (C)? The following lemma shows that if condition (C) is slightly modified, then the answer to the corresponding question is "no."

On the equation 𝑎𝑥-𝑥𝑏=𝑐 in division rings