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A non-semiprime associative algebra with zero weak radical.

Abdelfattah Haily (1997)

Extracta Mathematicae

The weak radical, W-Rad(A) of a non-associative algebra A, has been introduced by A. Rodríguez Palacios in [3] in order to generalize the Johnson's uniqueness of norm theorem to general complete normed non-associative algebras (see also [2] for another application of this notion). In [4], he showed that if A is a semiprime non-associative algebra with DCC on ideals, then W-Rad(A) = 0. In the first part of this paper we give an example of a non-semiprime associative algebra A with DCC on ideals and...

A note on finitely generated ideal-simple commutative semirings

Vítězslav Kala, Tomáš Kepka (2008)

Commentationes Mathematicae Universitatis Carolinae

Many infinite finitely generated ideal-simple commutative semirings are additively idempotent. It is not clear whether this is true in general. However, to solve the problem, one can restrict oneself only to parasemifields.

A Note on Free Quantum Groups

Teodor Banica (2008)

Annales mathématiques Blaise Pascal

We study the free complexification operation for compact quantum groups, G → G c . We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying G = G c .

A note on Frobenius divided modules in mixed characteristics

Pierre Berthelot (2012)

Bulletin de la Société Mathématique de France

If X is a smooth scheme over a perfect field of characteristic p , and if 𝒟 X ( ∞ ) is the sheaf of differential operators on X [7], it is well known that giving an action of 𝒟 X ( ∞ ) on an 𝒪 X -module ℰ is equivalent to giving an infinite sequence of 𝒪 X -modules descending ℰ via the iterates of the Frobenius endomorphism of X [5]. We show that this result can be generalized to any infinitesimal deformation f : X → S of a smooth morphism in characteristic p , endowed with Frobenius liftings. We also show that it extends to adic...

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