Action of a monoid or a group on a set have always been of interest for mathematicians and computer scientists. Also, the algebraic theory of a particular type of automata (without outputs) is nothing but the action of a free monoid or a free semigroup on a set (of states). On the other hand, domain theory, which studies directed complete partially ordered sets, was introduced by Scott in the 1970s as a foundation for programming semantics and provides an abstract model of computation, and has grown into a respected field on the borderline between mathematics and computer science. In this paper, combining the above two notions, we consider actions of a semigroup (monoid or group) on directed complete posets and study the algebraic notion of injectivity with respect to monomorphisms and embeddings in the category so obtained.
کلید واژگان :Action of a monoid, directed complete poset, injective object.
ارزش ریالی : 600000 ریال
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