Products of idempotent endomorphisms of relatively free algebras with weak exchange properties

John Fountain; Victoria Gould

doi:10.1017/S0013091504000902

Products of idempotent endomorphisms of relatively free algebras with weak exchange properties

John Fountain, Victoria Gould

Mathematics

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

Abstract

If A is a stable basis algebra of rank n, then the set Sn-1 of endomorphisms of rank at most n - 1 is a subsemigroup of the endomorphism monoid of A. This paper gives a number of necessary and sufficient conditions for Sn-1 to be generated by idempotents. These conditions are satisfied by finitely generated free modules over Euclidean domains and by free left T-sets of finite rank, where T is cancellative monoid in which every finitely generated left ideal is principal.

Original language	English
Pages (from-to)	343-362
Number of pages	20
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	50
DOIs	https://doi.org/10.1017/S0013091504000902
Publication status	Published - Jun 2007

Keywords

basis
exchange property
endomorphism monoid
idempotents
INDEPENDENCE ALGEBRA
MATRICES
SEMIGROUPS

Access to Document

10.1017/S0013091504000902

http://www-users.york.ac.uk/~jbf1/prodidpts.pdf

Cite this

@article{7cedbfcfd1334fea999df2be59897ac6,

title = "Products of idempotent endomorphisms of relatively free algebras with weak exchange properties",

abstract = "If A is a stable basis algebra of rank n, then the set Sn-1 of endomorphisms of rank at most n - 1 is a subsemigroup of the endomorphism monoid of A. This paper gives a number of necessary and sufficient conditions for Sn-1 to be generated by idempotents. These conditions are satisfied by finitely generated free modules over Euclidean domains and by free left T-sets of finite rank, where T is cancellative monoid in which every finitely generated left ideal is principal.",

keywords = "basis, exchange property, endomorphism monoid, idempotents, INDEPENDENCE ALGEBRA, MATRICES, SEMIGROUPS",

author = "John Fountain and Victoria Gould",

year = "2007",

month = jun,

doi = "10.1017/S0013091504000902",

language = "English",

volume = "50",

pages = "343--362",

journal = "Proceedings of the Edinburgh Mathematical Society",

issn = "1464-3839",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Products of idempotent endomorphisms of relatively free algebras with weak exchange properties

AU - Fountain, John

AU - Gould, Victoria

PY - 2007/6

Y1 - 2007/6

N2 - If A is a stable basis algebra of rank n, then the set Sn-1 of endomorphisms of rank at most n - 1 is a subsemigroup of the endomorphism monoid of A. This paper gives a number of necessary and sufficient conditions for Sn-1 to be generated by idempotents. These conditions are satisfied by finitely generated free modules over Euclidean domains and by free left T-sets of finite rank, where T is cancellative monoid in which every finitely generated left ideal is principal.

AB - If A is a stable basis algebra of rank n, then the set Sn-1 of endomorphisms of rank at most n - 1 is a subsemigroup of the endomorphism monoid of A. This paper gives a number of necessary and sufficient conditions for Sn-1 to be generated by idempotents. These conditions are satisfied by finitely generated free modules over Euclidean domains and by free left T-sets of finite rank, where T is cancellative monoid in which every finitely generated left ideal is principal.

KW - basis

KW - exchange property

KW - endomorphism monoid

KW - idempotents

KW - INDEPENDENCE ALGEBRA

KW - MATRICES

KW - SEMIGROUPS

U2 - 10.1017/S0013091504000902

DO - 10.1017/S0013091504000902

M3 - Article

SN - 1464-3839

VL - 50

SP - 343

EP - 362

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

ER -