Semigroups of transformations restricted by an equivalence

• Autorzy: Suzana Mendes-Gonçalves , Robert Sullivan
• Języki publikacji: EN

Abstrakty

EN

Suppose σ is an equivalence on a set X and let E(X, σ) denote the semigroup (under composition) of all α: X → X such that σ ⊆ α ∘ α −1. Here we characterise Green’s relations and ideals in E(X, σ). This is analogous to recent work by Sullivan on K(V, W), the semigroup (under composition) of all linear transformations β of a vector space V such that W ⊆ ker β, where W is a fixed subspace of V.

Słowa kluczowe

EN

Transformation semigroup; Equivalence; Green’s relations; Ideals

Kategorie tematyczne

• 20M20: Semigroups of transformations, etc.

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 6
• Strony: 1120-1131

Daty

wydano

2010-12-01

online

2010-10-30

Twórcy

autor

Suzana Mendes-Gonçalves

• Universidade do Minho,

autor

Robert Sullivan

• University of Western Australia,

Bibliografia

• [1] Clifford A.H., Preston G.B., The Algebraic Theory of Semigroups, Vol. 1 and 2, Math. Surveys Monogr., 7, American Mathematical Society, Providence, 1961 and 1967
• [2] Howie J.M., Fundamentals of Semigroup Theory, London Math. Soc. Monogr. Ser., 12, Clarendon Press, Oxford, 1995
• [3] Pei H., Regularity and Green’s relations for semigroups of transformations that preserve an equivalence, Comm. Algebra, 2005, 33(1), 109–118 http://dx.doi.org/10.1081/AGB-200040921
• [4] Pei H., Deng W., A note on Green’s relations in the semigroups T(X, ρ), Semigroup Forum, 2009, 79(1), 210–213 http://dx.doi.org/10.1007/s00233-009-9151-3
• [5] Sullivan R.P., Semigroups of linear transformations with restricted range, Bull. Austral. Math. Soc., 2008, 77(3), 441–453 http://dx.doi.org/10.1017/S0004972708000385
• [6] Sullivan R.P., Semigroups of linear transformations with restricted kernel (submitted)

Identyfikatory

DOI

10.2478/s11533-010-0066-8