Matrix relation algebras

M. El Bachraoui; M. Van de Vel

doi:10.1007/s000120200001

Matrix relation algebras

M. El Bachraoui, M. Van de Vel

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

3 Citations (Scopus)

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
Number of pages	27
Journal	Algebra Universalis
Volume	48
Issue number	3
DOIs	https://doi.org/10.1007/s000120200001
Publication status	Published - 2002
Externally published	Yes

Keywords

First-order property
Matrix relation algebra
Relativization

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s000120200001

Cite this

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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.",

keywords = "First-order property, Matrix relation algebra, Relativization",

author = "{El Bachraoui}, M. and {Van de Vel}, M.",

year = "2002",

doi = "10.1007/s000120200001",

language = "English",

volume = "48",

pages = "273--299",

journal = "Algebra Universalis",

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publisher = "Birkhauser Verlag Basel",

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TY - JOUR

T1 - Matrix relation algebras

AU - El Bachraoui, M.

AU - Van de Vel, M.

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.

KW - First-order property

KW - Matrix relation algebra

KW - Relativization

UR - http://www.scopus.com/inward/record.url?scp=0037000191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037000191&partnerID=8YFLogxK

U2 - 10.1007/s000120200001

DO - 10.1007/s000120200001

M3 - Article

AN - SCOPUS:0037000191

SN - 0002-5240

VL - 48

SP - 273

EP - 299

JO - Algebra Universalis

JF - Algebra Universalis

IS - 3

ER -

Matrix relation algebras

Abstract

Keywords

ASJC Scopus subject areas

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