In this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.
Sabadini, I., Struppa, D.C. Total Differentiability and Monogenicity for Functions in Algebras of Order 4. Complex Anal. Oper. Theory 15, 26 (2021). https://doi.org/10.1007/s11785-020-01069-0
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