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ON THE m-POTENT RANKS OF CERTAIN SEMIGROUPS OF ORIENTATION PRESERVING TRANSFORMATIONS
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 Title & Authors
ON THE m-POTENT RANKS OF CERTAIN SEMIGROUPS OF ORIENTATION PRESERVING TRANSFORMATIONS
Zhao, Ping; You, Taijie; Hu, Huabi;
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 Abstract
It is known that the ranks of the semigroups , and (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on , respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of and are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups , and . Firstly, we characterize the structure of the minimal generating sets of . As applications, we obtain that the number of distinct minimal generating sets is . Secondly, we show that, for , the m-potent ranks of the semigroups and are also n and 2n, respectively. Finally, we find that the 2-potent rank of is n + 1.
 Keywords
transformation;orientation-preserving;rank;idempotent rank;m-potent rank;
 Language
English
 Cited by
1.
On the (m, r)-potent ranks of certain semigroups of transformations, Journal of Algebra and Its Applications, 2016, 15, 01, 1650018  crossref(new windwow)
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