On Zariski spaces of free acts over semigroups
Mohammad Ali Naghipoor · Journal of Algebra and Its Applications · 2023
This study is concerned with the collections of prime and radical subacts of free acts over a semigroup [Formula: see text] The collection of all prime subacts of any free act is topologized with two topologies as generalizations of the notion of the Zariski topology in rings and semigroups. Moreover, the interplay between some algebraic properties and some topological properties of the spectrum of free acts is investigated. In particular, the conditions under which the set of all prime subacts of free acts is a spectral space are studied. Also, it is shown that a certain type of Zariski space of free acts is isomorphic to a lattice of radical subacts.