Gelfand-Kirillov dimension of some primitive abundant semigroups

Ranran Cui () and Yanfeng Luo
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Ranran Cui: Lanzhou University
Yanfeng Luo: Lanzhou University

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 6, 809-822

Abstract: 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).

Keywords: Gelfand-Kirillov dimension; primitively decomposable abundant semigroup; primitive regular semigroup; completely 0-simple semigroup; inverse monoid (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0044-5

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