Comapactness Conditions in Universal Algebraic Geometry
  In this article, the properties of being equational noetherian, $q_{\omega}$ and $u_{\omega}$-compactness, and equational Artinian are studied from the perspective of the Zariski topology. The equational conditions on the relative free algebras of arbitrary varieties are also investigated. 
P. Modabberi and M. Shahryari
math.RA