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

Let R be a ring, and be an endomorphism of R. An additive mapping H : R ! R is called a left -multiplier (centralizer) if H(xy) = H(x) (y) holds for all x;y 2 R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left -multipliers satisfying any one of the properties: (i) H((x;y)) (x;y) = 0; (ii) H((x;y))+ (x;y) = 0; (iii) H(x ◦y) x ◦y = 0; (iv) H(x ◦y)+x ◦y = 0; (v) H(xy) = xy; (vi) H(xy) = yx; (vii) H(x 2 ) = x 2 ; (viii) H(x 2 ) = x 2 for all x;y in some appropriate subset of R.

ON LEFT α-MULTIPLIERS AND COMMUTATIVITY OF SEMIPRIME RINGS