# Locally adequate semigroup algebras

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 29-48
- ISSN: 2391-5455

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topYingdan 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 -

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