Abstract
Let S be an algebraic semigroup (not necessarily linear) defined over a field F. We show that there exists a positive integer n such that x n belongs to a subgroup of S(F) for any x∈S(F). In particular, the semigroup S(F) is strongly π-regular.
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References
Brion, M.: On algebraic semigroups and monoids. In: Can, M., Li, Z., Steinberg, B., Wang, Q. (eds.) Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics. Fields Institute Communications. Springer, New York (2014)
Putcha, M.S.: Linear Algebraic Monoids. Cambridge University Press, Cambridge (1988)
Springer, T.A.: Linear Algebraic Groups, 2nd edn. Birkhäuser, Boston (1998)
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Brion, M., Renner, L.E. (2014). Algebraic Semigroups Are Strongly π-Regular. In: Can, M., Li, Z., Steinberg, B., Wang, Q. (eds) Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics. Fields Institute Communications, vol 71. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0938-4_2
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DOI: https://doi.org/10.1007/978-1-4939-0938-4_2
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