TY - JOUR
TI - Non-generators in extensions of infinitary algebras
AU - Lipparini, Paolo
TI - Non-generators in extensions of infinitary algebras
AB - 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.
VL - 2022
IS - Number 57
PY - 2022
SN - 0137-2904
C1 - 2084-2589
SP - 31
EP - 43
DO - 10.4467/20842589RM.22.002.16659
UR - https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/non-generators-in-extensions-of-infinitary-algebras
KW - non-generator
KW - infinitary algebra