DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

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Discussiones Mathematicae General Algebra and Applications 24(2) (2004) 267-275
DOI: https://doi.org/10.7151/dmgaa.1089

ON VARIETIES OF LEFT DISTRIBUTIVE LEFT IDEMPOTENT GROUPOIDS

David Stanovský

Charles University in Prague,
KA MFF UK, Sokolovská 83,
18675 Praha, Czech Republic
e-mail: stanovsk@karlin.mff.cuni.cz

Abstract

We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) » (xy)(xz) and (xx)y » xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity xn » x decomposes as the direct product of its largest idempotent factor and a cycle. Some properties of subdirectly ireducible LDLI groupoids are found.

Keywords: left distributivity, left idempotence, right zero band, LDLI groupoids, subdirectly irreducible, free groupoid, lattice of subvarieties.

2000 Mathematics Subject Classification: 08B15, 08B20, 08B26, 20N02.

References

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Received 13 August 2004
Revised 30 December 2004

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