Research output: Contribution to journal › Article › peer-review

**Extensions and covers for semigroups whose idempotents form a left regular band.** / Branco, Mario J. J.; Gomes, Gracinda M. S.; Gould, Victoria.

Research output: Contribution to journal › Article › peer-review

Branco, MJJ, Gomes, GMS & Gould, V 2010, 'Extensions and covers for semigroups whose idempotents form a left regular band', *Semigroup forum*, vol. 81, no. 1, pp. 51-70. https://doi.org/10.1007/s00233-010-9239-9

Branco, M. J. J., Gomes, G. M. S., & Gould, V. (2010). Extensions and covers for semigroups whose idempotents form a left regular band. *Semigroup forum*, *81*(1), 51-70. https://doi.org/10.1007/s00233-010-9239-9

Branco MJJ, Gomes GMS, Gould V. Extensions and covers for semigroups whose idempotents form a left regular band. Semigroup forum. 2010 Aug;81(1):51-70. https://doi.org/10.1007/s00233-010-9239-9

@article{642778cb40e9489287770b669555fdbf,

title = "Extensions and covers for semigroups whose idempotents form a left regular band",

abstract = "Proper extensions that are {"}injective on a{"}'-related idempotents{"} of a{"}>-unipotent semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and congruence conditions, referred to here as glrac semigroups, are described as certain subalgebras of a lambda-semidirect product of a left regular band by an a{"}>-unipotent or by a glrac semigroup, respectively. An example of such is the generalized Szendrei expansion.As a consequence of our embedding, we are able to give a structure theorem for proper left restriction semigroups. Further, we show that any glrac semigroup S has a proper cover that is a semidirect product of a left regular band by a monoid, and if S is left restriction, the left regular band may be taken to be a semilattice.",

keywords = "Expansions, R-unipotent semigroups, Generalised restriction, LEFT AMPLE SEMIGROUPS, UNIPOTENT SEMIGROUP, INVERSE-SEMIGROUPS, EXPANSION, MONOIDS",

author = "Branco, {Mario J. J.} and Gomes, {Gracinda M. S.} and Victoria Gould",

year = "2010",

month = aug,

doi = "10.1007/s00233-010-9239-9",

language = "English",

volume = "81",

pages = "51--70",

journal = "Semigroup forum",

issn = "0037-1912",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Extensions and covers for semigroups whose idempotents form a left regular band

AU - Branco, Mario J. J.

AU - Gomes, Gracinda M. S.

AU - Gould, Victoria

PY - 2010/8

Y1 - 2010/8

N2 - Proper extensions that are "injective on a"'-related idempotents" of a">-unipotent semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and congruence conditions, referred to here as glrac semigroups, are described as certain subalgebras of a lambda-semidirect product of a left regular band by an a">-unipotent or by a glrac semigroup, respectively. An example of such is the generalized Szendrei expansion.As a consequence of our embedding, we are able to give a structure theorem for proper left restriction semigroups. Further, we show that any glrac semigroup S has a proper cover that is a semidirect product of a left regular band by a monoid, and if S is left restriction, the left regular band may be taken to be a semilattice.

AB - Proper extensions that are "injective on a"'-related idempotents" of a">-unipotent semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and congruence conditions, referred to here as glrac semigroups, are described as certain subalgebras of a lambda-semidirect product of a left regular band by an a">-unipotent or by a glrac semigroup, respectively. An example of such is the generalized Szendrei expansion.As a consequence of our embedding, we are able to give a structure theorem for proper left restriction semigroups. Further, we show that any glrac semigroup S has a proper cover that is a semidirect product of a left regular band by a monoid, and if S is left restriction, the left regular band may be taken to be a semilattice.

KW - Expansions

KW - R-unipotent semigroups

KW - Generalised restriction

KW - LEFT AMPLE SEMIGROUPS

KW - UNIPOTENT SEMIGROUP

KW - INVERSE-SEMIGROUPS

KW - EXPANSION

KW - MONOIDS

UR - http://www.scopus.com/inward/record.url?scp=77954860335&partnerID=8YFLogxK

U2 - 10.1007/s00233-010-9239-9

DO - 10.1007/s00233-010-9239-9

M3 - Article

VL - 81

SP - 51

EP - 70

JO - Semigroup forum

JF - Semigroup forum

SN - 0037-1912

IS - 1

ER -