On simple anti-flexible rings

Commutative associative rings and anti-flexible rings

“…In order to prove that & is a simple anti-flexible ring, by Theorem 3.11 of [1] it suffices to show that the bilinear form <( , )> satifies the following conditions:…”

“…The results mentioned above of Anderson and Outcalt appear in [1]. In [3], Slater has shown that in semi-prime alternative rings the Nucleus and the center of an ideal of R are contained in the Nucleus the center of R respectively, which turns out to be very valuable in the structure theory of such rings.…”

Braided anti-flexible bialgebras

“…As a special type of Lie-admissible algebras, anti-flexible algebras have been studied by Anderson, Outcalt, Kosier and Rodabaugh in [7,16,23]. Recently, the concept of anti-flexible bialgebras is introduced by Dassoundo, Bai and Hounkonnou in [11].…”