Partial action - Open Access .click

International Journal of Algebra and Computation, 2004
A partial action of a group G on a set X is a weakening of the usual notion of a group action: the function G×X→X that defines a group action is replaced by a partial function; in addition, the existence of g·(h·x) implies the existence of (gh)·x, but not necessarily conversely.
Johannes Kellendonk, Mark V. Lawson
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Actions and partial actions of inductive constellations

Semigroup Forum, 2010
A semigroup \(S\) possessing a unary operation \(^+\) is called a `left restriction semigroup' if (in addition to the associative law) it satisfies the following identities: \(s^+s=s\); \(s^+t^+=t^+s^+\); \((s^+t)^+=s^+t^+\); \(st^+=(st)^+s\). Left restriction semigroups possess a natural partial order given by \(s\leq t\Leftrightarrow s=s^+t\).
Gould, Victoria, Hollings, Christopher
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PARTIAL GROUP ACTIONS ON SEMIALGEBRAS

Asian-European Journal of Mathematics, 2012
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.
Sharma, Ram Parkash, Anu, Singh, Nirmal
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partial actions
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