Locally adequate semigroup algebras

Yingdan Ji, and Yanfeng Luo. "Locally adequate semigroup algebras." Open Mathematics 14.1 (2016): 29-48. <http://eudml.org/doc/276953>.

@article{YingdanJi2016,
abstract = {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*$0\{\rm \{ - \}\}\{\mathcal \{J\}\}*$-simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the [...] ℛ*$\{\mathcal \{R\}\}*$-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.},
author = {Yingdan Ji, Yanfeng Luo},
journal = {Open Mathematics},
keywords = {Contracted semigroup algebras; Rukolaĭne idempotents; Multiplicative basis; Direct product decomposition; Representation type; contracted semigroup algebras; multiplicative basis; direct product decomposition; representation type},
language = {eng},
number = {1},
pages = {29-48},
title = {Locally adequate semigroup algebras},
url = {http://eudml.org/doc/276953},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Yingdan Ji
AU - Yanfeng Luo
TI - Locally adequate semigroup algebras
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 29
EP - 48
AB - 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*$0{\rm { - }}{\mathcal {J}}*$-simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the [...] ℛ*${\mathcal {R}}*$-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.
LA - eng
KW - Contracted semigroup algebras; Rukolaĭne idempotents; Multiplicative basis; Direct product decomposition; Representation type; contracted semigroup algebras; multiplicative basis; direct product decomposition; representation type
UR - http://eudml.org/doc/276953
ER -