Abstract
Subdirectly irreducible acts and finitely subdirectly irreducible acts are characterized, for acts over a commutative semigroup that satisfy finiteness conditions.
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G. Birkhoff, Subdirect unions in universal algebra, Bull. Amer. Math. Soc., 50 (1944), 764–768.
L. Budach, Struktur Noetherscher kommutativer Halbgruppen, Monatsb. Deutsch. Akad. Wiss. Berlin, 6 (1964), 85–88.
S. Eilenberg, Automata, Languages, and Machines, Vol. B, Academic Press, 1976.
P. A. Grillet, On subdirectly irreducible commutative semigroups, Pacific J. Math., 69 (1977), 55–71.
P. A. Grillet, Commutative semigroups, Kluwer Acad. Publ., Dordrecht, 2001.
P. A. Grillet, Cancellative coextensions, Acta Sci. Math. (Szeged), 69 (2003), 543–567.
P. A. Grillet, Commutative actions, Acta Sci. Math. (Szeged), to appear.
A. I. Malcev, On homomorphisms onto finite groups, Uch. Zap. Ivanov. Gos. Ped. Inst., 18 (1958), 49–60 (in Russian).
B. M. Schein, Homomorphisms and subdirect decompositions of semigroups, Pacific J. Math., 17 (1966), 529–547.
B. Stenström, Flatness and localization over monoids, Math. Nachr., 48 (1971), 315–334.
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Communicated by Mária B. Szendrei
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Grillet, P.A. Irreducible actions. Period Math Hung 54, 51–76 (2007). https://doi.org/10.1007/s-10998-007-1051-4
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DOI: https://doi.org/10.1007/s-10998-007-1051-4