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TitleNilpotents and congruences on semigroups of transformations with fixed rank
Author(s)Smith, M. Paula Marques
Sullivan, R. P.
KeywordsNilpotent transformations
Issue date1995
PublisherCambridge University Press
JournalProceedings of the Royal Society of Edinburgh
Abstract(s)In1998, Howie and Marques-Smith studied Pm, a Rees quotient semigroup of transformations associated with a regular cardinal m, and described the elements which can be written as a product of nilpotents in Pm. In 1981, Marques proved that if ∆m denotes the Malcev congruence on Pm, then Pm/∆m is congruence-free for any infinite m. In this paper, we describe the products of nilpotentes in Pm, when m is non-regular, and determine all the congruences on Pm when m is an arbitrary infinite cardinal. We also investigate when a nilpotent is a product of idempotents.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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