Quasi-semi-homomorphisms and generalized proximity relations between Boolean algebras

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Semi-Cohen Boolean Algebras

We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semi-Cohen algebras, pseudo-Cohen algebras and potentially Cohen algebras. These classes of Boolean algebras are closed under completion.

On Semi-boolean-like Algebras

In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra A with constants 0, 1 is Booolean-like in case for all a ∈ A the congruences θ (a, 0) and θ (a, 1) are compementary factor congruences of A. We also introduced the weaker notion of semi-Boolean-like algebra, showin...

Homomorphisms between Solomon's Descent Algebras

In a previous paper (see Garsia-Reutenauer [2]), we have studied algebraic properties of the descent algebras Σ n , and shown how these are related to the canonical decomposition of the free Lie algebra corresponding to a version of Poincaré-Birkhoff-Witt's theorem. In the present paper, we study homomorphisms between these algebras Σ n. The existence of these homomorphisms was suggested by pro...

Dually quasi-De Morgan Stone semi-Heyting algebras I. Regularity

This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...