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- W3100554770 abstract "The variant of a semigroup [Formula: see text] with respect to an element [Formula: see text], denoted [Formula: see text], is the semigroup with underlying set [Formula: see text] and operation ⋆ defined by [Formula: see text] for [Formula: see text]. In this paper, we study variants [Formula: see text] of the full transformation semigroup [Formula: see text] on a finite set [Formula: see text]. We explore the structure of [Formula: see text] as well as its subsemigroups [Formula: see text] (consisting of all regular elements) and [Formula: see text] (consisting of all products of idempotents), and the ideals of [Formula: see text]. Among other results, we calculate the rank and idempotent rank (if applicable) of each semigroup, and (where possible) the number of (idempotent) generating sets of the minimal possible size." @default.
- W3100554770 created "2020-11-23" @default.
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- W3100554770 date "2015-12-01" @default.
- W3100554770 modified "2023-09-26" @default.
- W3100554770 title "Variants of finite full transformation semigroups" @default.
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- W3100554770 doi "https://doi.org/10.1142/s021819671550037x" @default.
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