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Noah Schweber
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A finite algebra in a finite language has finite essential arity if and only if it is strongly nilpotent. This is proved in Section 4 of:

Keith A. Kearnes and Emil W. Kiss, Finite algebras of finite complexityFinite algebras of finite complexity. Discrete Math. 207 (1999), 89--135.

A finite algebra in a finite language has finite essential arity if and only if it is strongly nilpotent. This is proved in Section 4 of:

Keith A. Kearnes and Emil W. Kiss, Finite algebras of finite complexity. Discrete Math. 207 (1999), 89--135.

A finite algebra in a finite language has finite essential arity if and only if it is strongly nilpotent. This is proved in Section 4 of:

Keith A. Kearnes and Emil W. Kiss, Finite algebras of finite complexity. Discrete Math. 207 (1999), 89--135.

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Keith Kearnes
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A finite algebra in a finite language has finite essential arity if and only if it is strongly nilpotent. This is proved in Section 4 of:

Keith A. Kearnes and Emil W. Kiss, Finite algebras of finite complexity. Discrete Math. 207 (1999), 89--135.