Math Essentials' Algebra volume was voted the third most popular algebra textbook by aA recent comprehensive Wiki pollA that surveyed hundreds of similar textbooks.

The Hopf algebra H* becomes a right and left H-module by the hit actions [??] [??] defined for all a [member of] H, p [member of] H*,

Every left coideal subalgebra of H is semisimple as an algebra and equipped with a 1-dimensional ideal of integrals, we denote by [[and].sub.N] the unique idempotent integral of N.

where the maps [j.sub.*] and [[pi].sub.*] are induced by the chain maps, on the chain level, [mathematical expression not reproducible], respectively, and U[([g.sub.n]).sup.ad] is the adjoint universal enveloping algebra of [g.sub.n].

Let R be a nonempty set together with two binary operations "+" and "*" which satisfies all the axioms of an associative ring (algebra) except an associative property with respect to multiplication; then, it is known as a nonassociative ring (algebra).