Partial actions and proper extensions of two-sided restriction semigroups

Mikhailo Dokuchaev, Mykola Khrypchenko, Ganna Kudryavtseva

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study several classes of partial actions of two-sided restriction semigroups that generalize partial actions of monoids and of inverse semigroups. We establish an adjunction between the category P(S) of proper extensions of a restriction semigroup S and a category A(S) of partial actions of S subject to certain conditions going back to the work of O'Carroll. In the category A(S), we specify two isomorphic subcategories, one being reflective and the other one coreflective, each of which is equivalent to the category P(S).

Original languageEnglish
Article number106649
JournalJournal Of Pure And Applied Algebra
Issue number9
Publication statusPublished - Sept 2021


  • Expansion
  • Inverse monoid
  • Partial action
  • Prefix group expansion
  • Premorphism
  • Restriction monoid


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