Non-generators in extensions of infinitary algebras

• Autorzy: Lipparini Paolo

Identyfikatory

DOI

10.4467/20842589RM.22.002.16659

• Języki publikacji: EN

Abstrakty

EN

Contrary to the finitary case, the set Γ(A) of all the non-generators of an infinitary algebra A is not necessarily a subalgebra of A. We show that the phenomenon is ubiquitous: every algebra with at least one infinitary operation can be embedded into some algebra B such that Γ(B) is not a subalgebra of B. As far as expansions are concerned, there are examples of infinite algebras A such that in every expansion B of A the set Γ(B) is a subalgebra of B. However, under relatively weak assumptions on A, it is possible to get some expansion B of A such that Γ(B) fails to be a subalgebra of B.

Słowa kluczowe

EN

non-generator; infinitary algebra

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2022
• Tom: Vol. 57
• Strony: 31--43
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Lipparini Paolo

• Dipartimento di Matematica Viale della Ricerca Non Generatrice Universitá di Roma “Tor Vergata” I-00133 Rome Italy, http://www.mat.uniroma2.it/ lipparin

Bibliografia

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• [3] G. E. Hansoul, The Frattini subalgebra of an infinitary algebra, Bull. Soc. Roy. Sci. Li`ege 49 (1980), 423–424.
• [4] G. Janelidze, Frattini subobjects and extensions in semi-Abelian categories, Bull. Iranian Math. Soc. 44 (2018), 291–304.
• [5] E. W. Kiss and S.M. Vovsi, Critical algebras and the Frattini congruence, Algebra Universalis 34 (1995), 336–344.
• [6] P. Lipparini, Non-generators in complete lattices and semilattices, Acta Math. Hungar. 166 (2022), 423–431.
• [7] H. Rubin and J.E. Rubin,, Equivalents of the axiom of choice. II, Studies in Logic and the Foundations of Mathematics, 116, North-Holland Publishing Co., Amsterdam (1985).

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).