Epimorphisms are not surjective, even in simple algebras
Using techniques developed by Comer on sheaf-theoretic duality for cylindric algebras, we refine a result of Judit Madarasz by showing that epimorphisms are not surjective even in the class of simple infinite dimensional cylindric algebras.
The class of infinite dimensional quasipolaydic equality algebras is not finitely axiomatizable over its diagonal free reducts
We show that the class of infinite dimensional quasipolaydic equality algebras is not finitely axiomatizable over its diagonal free reducts
Normed units in abelian group rings
We compute explicitly the isomorphic structure of the normalized unit group of an abelian group ring under some minimal natural restrictions on the group basis and the coefficient ring. This enlarges affirmations due to Chatzidakis-Pappas (J. London Math. Soc., 1991) and Mollov (Publ. Math. Debrecen, 1971).