A Note on Semigroup Algebras of Permutable Semigroups |
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Authors: | A Nagy M Zubor |
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Institution: | 1. Department of Algebra, Mathematical Institute, Budapest University of Technology and Economics, Budapestnagyat@math.bme.hu;3. Department of Algebra, Mathematical Institute, Budapest University of Technology and Economics, Budapest |
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Abstract: | Let S be a semigroup and 𝔽 be a field. For an ideal J of the semigroup algebra 𝔽S] of S over 𝔽, let ?J denote the restriction (to S) of the congruence on 𝔽S] defined by the ideal J. A semigroup S is called a permutable semigroup if α ○ β = β ○ α is satisfied for all congruences α and β of S. In this paper we show that if S is a semilattice or a rectangular band then φ{S; 𝔽}: J → ?J is a homomorphism of the semigroup (Con(𝔽S]); ○ ) into the relation semigroup (?S; ○ ) if and only if S is a permutable semigroup. |
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Keywords: | Lattice of congruences Permutable semigroup Semigroup algebra |
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