Abstract
In this paper, the growth and Gelfand-Kirillov dimension of some primitive abundant semigroups are investigated. It is shown that for certain primitive abundant (regular) semigroup S, S as well as the semigroup algebra K [S] has polynomial growth if and only if all of its cancellative submonoids (subgroups) T as well as K[T] have polynomial growth. As applications, it is shown that if S is a finitely generated primitive inverse monoid having the permutational property, then clK dim K[S] = GK dim K[S] = rk(S).
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This research was partially supported by the National Natural Science Foundation of China (No. 10971086)
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Cui, R., Luo, Y. Gelfand-Kirillov dimension of some primitive abundant semigroups. Indian J Pure Appl Math 44, 809–822 (2013). https://doi.org/10.1007/s13226-013-0044-5
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DOI: https://doi.org/10.1007/s13226-013-0044-5