Locally adequate semigroup algebras
We 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 abundant 0-J*$0{\rm{ - }}{\cal J}*$-simple semigroup algebras...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-01-01
|
| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/math.2016.14.issue-1/math-2016-0004/math-2016-0004.xml?format=INT |
| Summary: | We 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 abundant 0-J*$0{\rm{ - }}{\cal J}*$-simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the ℛ*${\cal R}*$-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. |
|---|---|
| ISSN: | 2391-5455 |