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.

Lipparini, P. (2022). Non-generators in extensions of infinitary algebras. REPORTS ON MATHEMATICAL LOGIC, 57, 31-43 [10.4467/20842589RM.22.002.16659].

Non-generators in extensions of infinitary algebras

Lipparini, P
2022-01-01

Abstract

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.
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
non-generator; infinitary algebra
Lipparini, P. (2022). Non-generators in extensions of infinitary algebras. REPORTS ON MATHEMATICAL LOGIC, 57, 31-43 [10.4467/20842589RM.22.002.16659].
Lipparini, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/277569
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