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- W4313598505 abstract "A set-theoretical solution of the pentagon equation on a non-empty set $X$ is a function $s:Xtimes Xto Xtimes X$ satisfying the relation $s_{23}, s_{13}, s_{12}=s_{12}, s_{23}$, with $s_{12}=stimes ,id_X$, $s_{23}=id_X times , s$ and $s_{13}=(id_Xtimes , tau)s_{12}(id_Xtimes ,tau)$, where $tau:Xtimes Xto Xtimes X$ is the flip map given by $tau(x,y)=(y,x)$, for all $x,yin X$. Writing a solution as $s(x,y)=(xy ,theta_x(y))$, where $theta_x: X to X$ is a map, for every $xin X$, one has that $X$ is a semigroup. In this paper, we study idempotent solutions, i.e., $s^2=s$, by showing that the idempotents of $X$ have a key role in such an investigation. In particular, we describe all such solutions on monoids having central idempotents. Moreover, we focus on idempotent solutions defined on monoids for which the map $theta_1$ is a monoid homomorphism." @default.
- W4313598505 created "2023-01-06" @default.
- W4313598505 creator A5068668696 @default.
- W4313598505 date "2023-01-04" @default.
- W4313598505 modified "2023-10-01" @default.
- W4313598505 title "Idempotent set-theoretical solutions of the pentagon equation" @default.
- W4313598505 doi "https://doi.org/10.1007/s40574-023-00382-8" @default.
- W4313598505 hasPublicationYear "2023" @default.
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