[1]
Abadie, F., ‘Enveloping actions and Takai duality for partial actions’, J. Funct. Anal.
197(1) (2003), 14–67.
[2]
Adámek, J. and Trnková, V., Automata and Algebras in Categories, Mathematics and its Applications, 37 (Kluwer Academic Publishers, Dordrecht, 1990).
[3]
Clifford, A. and Preston, G., The Algebraic Theory of Semigroups, Mathematical Surveys and Monographs 7, 1 (American Mathematical Society, Providence, RI, 1961).
[4]
Cohn, P. M., Universal Algebra, 2nd edn, Vol. 6 (Reidel Publishing Co., Dordrecht–Boston, MA, 1981).
[5]
Dokuchaev, M., del Río, Á. and Simón, J. J., ‘Globalizations of partial actions on nonunital rings’, Proc. Amer. Math. Soc.
135(2) (2007), 343–352.
[6]
Dokuchaev, M. and Exel, R., ‘Associativity of crossed products by partial actions, enveloping actions and partial representations’, Trans. Amer. Math. Soc.
357(5) (2005), 1931–1952.
[7]
Dokuchaev, M. and Novikov, B., ‘Partial projective representations and partial actions’, J. Pure Appl. Algebra
214(3) (2010), 251–268.
[8]
Exel, R., ‘Partial actions of groups and actions of inverse semigroups’, Proc. Amer. Math. Soc.
126(12) (1998), 3481–3494.
[9]
Ferrero, M., ‘Partial actions of groups on semiprime rings’, in: Groups, Rings and Group Rings, Lecture Notes in Pure and Applied Mathematics, 248 (Chapman & Hall/CRC, Boca Raton, FL, 2006), 155–162.
[10]
Grätzer, G., Universal Algebra, 2nd edn (Springer, New York, 2008).
[11]
Grillet, P. A. and Petrich, M., ‘Free products of semigroups amalgamating an ideal’, J. Lond. Math. Soc. (2)
2 (1970), 389–392.
[12]
Kellendonk, J. and Lawson, M. V., ‘Partial actions of groups’, Internat. J. Algebra Comput.
14(1) (2004), 87–114.
[13]
Ljapin, E. S. and Evseev, A. E., The Theory of Partial Algebraic Operations, Mathematics and its Applications, 414 (Springer Science+Business Media, B.V., Dordrecht, 1997).
[14]
Mac Lane, S., Categories for the Working Mathematician (Springer, New York–Heidelberg–Berlin, 1971).
[15]
Mal’cev, A. I., Algebraic Systems (Springer, Berlin–Heidelberg–New York, 1973).
[16]
Neumann, H., ‘Generalized free products with amalgamated subgroups I’, Amer. J. Math.
70 (1948), 590–625.
[17]
Neumann, H., ‘Generalized free products with amalgamated subgroups II’, Amer. J. Math.
71 (1949), 491–540.
[18]
Neumann, H., ‘Generalized free sums of cyclical groups’, Amer. J. Math.
72 (1950), 671–685.
[19]
Neumann, H., ‘On an amalgam of Abelian groups’, J. Lond. Math. Soc. (2)
26 (1951), 228–232.
[20]
Neumann, B. H., ‘An essay on free products of groups with amalgamations’, Philos. Trans. R. Soc. Lond. Ser. A
246 (1954), 503–554.
[21]
Neumann, B. H. and Neumann, H., ‘A contribution to the embedding theory of group amalgams’, Proc. Lond. Math. Soc. (3)
3 (1953), 243–256.
[22]
Terese, Term Rewriting Systems, Cambridge Tracts in Theoretical Computer Science, 55(Cambridge University Press, Cambridge, 2003).
[23]
Tsalenko, M. Sh. and Shul’geĭfer, E. G., ‘Foundations of category theory’, Modern Algebra (Nauka, Moscow, 1974), (Russian).
$\unicode[STIX]{x1D703}$
of a group on a set with an algebraic structure, we construct a reflector of
$\unicode[STIX]{x1D703}$
in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In particular, if
$\unicode[STIX]{x1D703}$
is a partial action on an algebra from a variety
$\mathsf{V}$
, then we show that the problem reduces to the embeddability of a certain generalized amalgam of
$\mathsf{V}$
-algebras associated with
$\unicode[STIX]{x1D703}$
. As an application, we describe globalizable partial actions on semigroups, whose domains are ideals.