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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let $f$ and $g$ be two noncommutative polynomials in disjoint sets ofvariables. An algebra $A$ is verbally prime if whenever $f\cdot g$ is anidentity for $A$ then either $f$ or $g$ is also an identity. As an analogue ofthis property Regev proved that the verbally prime algebra $M_k(F)$ of $k\timesk$ matrices over an infinite field $F$ has the following primeness property forcentral polynomials: whenever the product $f\cdot g$ is a central polynomialfor $M_k(F)$ then both $f$ and $g$ are central polynomials. In this paper weprove that over a field of characteristic zero Regev' s result holds for theverbally prime algebras $M_k(E)$ and $M_{k,k}(E)$, where $E$ is the infinitedimensional Grassmann algebra.

Primeness property for central polynomials of verbally prime P.I. algebras