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*-simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the [...] 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.
@article{bwmeta1.element.doi-10_1515_math-2016-0004,
author = {Yingdan Ji and Yanfeng Luo},
title = {Locally adequate semigroup algebras},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {29-48},
zbl = {06632336},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0004}
}
Yingdan Ji; Yanfeng Luo. Locally adequate semigroup algebras. Open Mathematics, Tome 14 (2016) pp. 29-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0004/