Semigroups That Contain All Singular Transformations

André, Jorge

doi:10.1007/s00233-003-0006-z

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“…(Of course such presentations may be obtained by rewriting the defining relations from [8].) For further studies on T n \ S n , see for example [1,2,20].…”

Section: Introductionmentioning

confidence: 99%

On the Singular Part of the Partition Monoid

East

2011

Int. J. Algebra Comput.

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We study the singular part of the partition monoid [Formula: see text]; that is, the ideal [Formula: see text], where [Formula: see text] is the symmetric group. Our main results are presentations in terms of generators and relations. We also show that [Formula: see text] is idempotent generated, and that its rank and idempotent-rank are both equal to [Formula: see text]. One of our presentations uses an idempotent generating set of this minimal cardinality.

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“…(Of course such presentations may be obtained by rewriting the defining relations from [8].) For further studies on T n \ S n , see for example [1,2,20].…”

Section: Introductionmentioning

confidence: 99%