In this note, we show that Radford's formula for the fourth power of the antipode can be proven for any regular multiplier Hopf algebra with integrals (algebraic quantum groups). This of course not only includes the case of a finite-dimensional Hopf algebra but also the case of any Hopf algebra with integrals (co-Frobenius Hopf algebras). The proof follows in a few lines from well-known formula...

Introduction The aim of this note is to provide a Steiner triple system STS( v ) which admits a partition into v STS( v) for every v 1 or 3 (mod 6). The STS( v ) obtained in this way will also contain ~v( v 1) subsystems of order 3v. An analogous construction is provided of an S(2, 4, v ) with a partition into v S(2, 4, v)'s in the case v 1 (mod 12). The Steiner system constructed here will als...

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