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Discriminants of Chebyshev radical extensions

T. Alden Gassert (2014)

Journal de Théorie des Nombres de Bordeaux

Let t be any integer and fix an odd prime ℓ . Let Φ ( x ) = T ℓ n ( x ) - t denote the n -fold composition of the Chebyshev polynomial of degree ℓ shifted by t . If this polynomial is irreducible, let K = ℚ ( θ ) , where θ is a root of Φ . We use a theorem of Dedekind in conjunction with previous results of the author to give conditions on t that ensure K is monogenic. For other values of t , we apply a result of Guàrdia, Montes, and Nart to obtain a formula for the discriminant of K and compute an integral basis for the ring of integers...

Disjoint sequences in Boolean algebras

Ján Jakubík (1998)

Mathematica Bohemica

We deal with the system Conv B of all sequential convergences on a Boolean algebra B . We prove that if α is a sequential convergence on B which is generated by a set of disjoint sequences and if β is any element of Conv B , then the join α ∨ β exists in the partially ordered set Conv B . Further we show that each interval of Conv B is a Brouwerian lattice.

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