Monoids that have only invertible elements are called groups. Groups are the most important single structure in algebra and have enormous applications in physics as well.
CITATION STYLE
Mazzola, G., Mannone, M., & Pang, Y. (2016). Groups. In Computational Music Science (pp. 147–150). Springer Nature. https://doi.org/10.1007/978-3-319-42937-3_18
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