An Example in the Singer Category of Algebras with Coproducts at Odd Primes

In 2005, William M. Singer introduced the notion of k-algebra with coproducts for any commutative ring k, and showed that the algebra of operations on the cohomology ring of any cocommutative F2-Hopf algebra can be endowed with such structure. In this paper we show that the same is true when the ground field of the cocommutative Hopf algebra is Fp, p is any odd prime, and the algebra of operations B(p) is equipped with an exotic coproduct. We also give an explicit description of the coalgebra with products dual to B(p).