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Locally adequate semigroup algebras
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AbstractWe build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant0-J*$0{\rm{ - }}{\cal J}*$-simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of theℛ*${\cal R}*$-classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we provide a description of the projective indecomposable modules and determine the representation type.
Title: Locally adequate semigroup algebras
Description:
AbstractWe build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents.
This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant0-J*$0{\rm{ - }}{\cal J}*$-simple semigroup algebras.
We also deduce a direct sum decomposition of this semigroup algebra in terms of theℛ*${\cal R}*$-classes of the semigroup obtained from the above multiplicative basis.
Finally, for some special cases, we provide a description of the projective indecomposable modules and determine the representation type.
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