학술논문
Generalizations of free monoids
Document Type
Working Paper
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Abstract
We generalize free monoids by defining $k$-monoids. These are nothing other than the one-vertex higher-rank graphs used in $C^{\ast}$-algebra theory with the cardinality requirement waived. The $1$-monoids are precisely the free monoids. We then take the next step and generalize $k$-monoids in such a way that self-similar group actions yield monoids of this type.