PARTIAL GROUP ACTIONS ON SEMIALGEBRAS

Abstract

For defining a K-semialgebra A, we use Katsov's tensor product which makes the category K-Smod monoidal. Further, if A is a K-semialgebra then AΔ is a KΔ-algebra and A embeds in AΔ. The subtractive and strong partial actions of a group are defined on A. A subtractive partial action α of a group G on A can be extended to a partial action of G on AΔ which helps in globalization of α. A strong partial action on A has a unique subtractive globalization. We also discuss the associativity of the skew group semiring A ×α G.