Bases of identities for semigroups of bounded rank transformations of a set. (Q1760386)
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scientific article; zbMATH DE number 6105497
| Language | Label | Description | Also known as |
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| English | Bases of identities for semigroups of bounded rank transformations of a set. |
scientific article; zbMATH DE number 6105497 |
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Bases of identities for semigroups of bounded rank transformations of a set. (English)
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13 November 2012
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The 88-element semigroup \(T_2(4)\) is formed by all total transformations of a 4-element set whose images contain at most 2 elements. The author describes the identities holding in \(T_2(4)\) (Theorem~2) via a number of combinatorial conditions that, given an identity, can be checked in time bounded by a polynomial of the length of the identity. Using this description, the author shows that the identities of \(T_2(4)\) admit no finite basis (Proposition~3).
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finite semigroups
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varieties of semigroups
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finite identity bases
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transformation semigroups
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ranks of transformations
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bases of identities
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non-finitely based semigroups
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