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This paper is devoted to the study of typical properties (in the BaireCategory sense) of certain classes of continuous linear operators acting onFr\'echet algebras, endowed with the topology of pointwise convergence. Ourmain results show that within natural Polish spaces of continuous operatorsacting on the algebra $H(\mathbb{C})$ of entire functions on $\mathbb{C}$, atypical operator supports a hypercyclic algebra. We also investigate the caseof the complex Fr\'echet algebras $X=\ell_{p}(\mathbb{N})$, $1\le p<+\infty$,or $X=c_{0}(\mathbb{N})$ endowed with the coordinatewise product, and show thatwhenever $M>1$, a typical operator on $X$ of norm less than or equal to $M$admits a hypercyclic algebra.

Typicality of operators on Fr\'echet algebras admitting a hypercyclic algebra