Matrix relation algebras

M. el Bachraoui; M.L.J. van de Vel

doi:10.1007/s000120200001

Matrix relation algebras

M. el Bachraoui, M.L.J. van de Vel

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

Square matrices over a relation algebra are relation algebras in a natural way. We show that for fixed n, these algebras can be characterized as reducts of some richer kind of algebra. Hence for fixed n, the class of n × n matrix relation algebras has a first-order characterization. As a consequence, homomorphic images and proper extensions of matrix relation algebras are isomorphic to matrix relation algebras.

Original language	English
Pages (from-to)	273-299
Journal	Algebra Universalis
Volume	48
Issue number	3
DOIs	https://doi.org/10.1007/s000120200001
Publication status	Published - 2002

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MR1954776

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title = "Matrix relation algebras",

abstract = "Square matrices over a relation algebra are relation algebras in a natural way. We show that for fixed n, these algebras can be characterized as reducts of some richer kind of algebra. Hence for fixed n, the class of n × n matrix relation algebras has a first-order characterization. As a consequence, homomorphic images and proper extensions of matrix relation algebras are isomorphic to matrix relation algebras.",

author = "{el Bachraoui}, M. and {van de Vel}, M.L.J.",

note = "MR1954776 ",

year = "2002",

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language = "English",

volume = "48",

pages = "273--299",

journal = "Algebra Universalis",

issn = "0002-5240",

publisher = "Birkhauser Verlag Basel",

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T1 - Matrix relation algebras

AU - el Bachraoui, M.

AU - van de Vel, M.L.J.

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PY - 2002

Y1 - 2002

N2 - Square matrices over a relation algebra are relation algebras in a natural way. We show that for fixed n, these algebras can be characterized as reducts of some richer kind of algebra. Hence for fixed n, the class of n × n matrix relation algebras has a first-order characterization. As a consequence, homomorphic images and proper extensions of matrix relation algebras are isomorphic to matrix relation algebras.

AB - Square matrices over a relation algebra are relation algebras in a natural way. We show that for fixed n, these algebras can be characterized as reducts of some richer kind of algebra. Hence for fixed n, the class of n × n matrix relation algebras has a first-order characterization. As a consequence, homomorphic images and proper extensions of matrix relation algebras are isomorphic to matrix relation algebras.

U2 - 10.1007/s000120200001

DO - 10.1007/s000120200001

M3 - Article

VL - 48

SP - 273

EP - 299

JO - Algebra Universalis

JF - Algebra Universalis

SN - 0002-5240

IS - 3

ER -

Matrix relation algebras

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