The free non-commutative cylindric algebras are not atomic
Mohamed Khaled · Logic Journal of IGPL · 2016
The classes of non-commutative cylindric algebras and weakened cylindric algebras were shown, by István Németi, to have decidable equational theories. In this article, we give new proof for this result and we give an answer to the open problem, posed by Németin 1985, addressing the atomicity of the finitely generated free algebras of these classes. We prove that the free algebras of these classes are not atomic.