On certain Cross varieties of aperiodic monoids with commuting idempotents

Edmond W. H. Lee

doi:10.1007/s00025-014-0390-6

On certain Cross varieties of aperiodic monoids with commuting idempotents

Edmond W. H. Lee

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

13 Scopus citations

Abstract

Let A_com denote the class of aperiodic monoids with commuting idempotents. It is shown that any subvariety of A_com that satisfies the identity x²yx ≈ xyx² is Cross if and only if it excludes the almost Cross varieties J₁, J₂, and L. Consequently, these three almost Cross varieties are unique among all subvarieties of A_com that satisfy the identity x²yx ≈ xyx². On the other hand, the existence of almost Cross subvarieties of A_com different from J₁, J₂, and L is also established.

Original language	American English
Pages (from-to)	491–510
Journal	Results in Mathematics
Volume	66
Issue number	3–4
DOIs	https://doi.org/10.1007/s00025-014-0390-6
State	Published - Nov 2014

Bibliographical note

Publisher Copyright:
© 2014 Springer Basel.

ASJC Scopus Subject Areas

Mathematics (miscellaneous)

Keywords

Monoid
Aperiodic monoid
Commuting idempotents
Variety
Cross variety

Disciplines

Mathematics

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10.1007/s00025-014-0390-6

Cite this

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title = "On certain Cross varieties of aperiodic monoids with commuting idempotents",

abstract = "Let Acom denote the class of aperiodic monoids with commuting idempotents. It is shown that any subvariety of Acom that satisfies the identity x2yx ≈ xyx2 is Cross if and only if it excludes the almost Cross varieties J1, J2, and L. Consequently, these three almost Cross varieties are unique among all subvarieties of Acom that satisfy the identity x2yx ≈ xyx2. On the other hand, the existence of almost Cross subvarieties of Acom different from J1, J2, and L is also established.",

keywords = "Monoid, Aperiodic monoid, Commuting idempotents, Variety, Cross variety",

author = "Lee, \{Edmond W. H.\}",

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year = "2014",

month = nov,

doi = "10.1007/s00025-014-0390-6",

language = "American English",

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TY - JOUR

T1 - On certain Cross varieties of aperiodic monoids with commuting idempotents

AU - Lee, Edmond W. H.

PY - 2014/11

Y1 - 2014/11

N2 - Let Acom denote the class of aperiodic monoids with commuting idempotents. It is shown that any subvariety of Acom that satisfies the identity x2yx ≈ xyx2 is Cross if and only if it excludes the almost Cross varieties J1, J2, and L. Consequently, these three almost Cross varieties are unique among all subvarieties of Acom that satisfy the identity x2yx ≈ xyx2. On the other hand, the existence of almost Cross subvarieties of Acom different from J1, J2, and L is also established.

AB - Let Acom denote the class of aperiodic monoids with commuting idempotents. It is shown that any subvariety of Acom that satisfies the identity x2yx ≈ xyx2 is Cross if and only if it excludes the almost Cross varieties J1, J2, and L. Consequently, these three almost Cross varieties are unique among all subvarieties of Acom that satisfy the identity x2yx ≈ xyx2. On the other hand, the existence of almost Cross subvarieties of Acom different from J1, J2, and L is also established.

KW - Monoid

KW - Aperiodic monoid

KW - Commuting idempotents

KW - Variety

KW - Cross variety

UR - http://www.webofscience.com/wos/woscc/full-record/WOS:000344346500013

UR - https://www.scopus.com/pages/publications/84948381223

UR - https://www.scopus.com/pages/publications/84948381223#tab=citedBy

U2 - 10.1007/s00025-014-0390-6

DO - 10.1007/s00025-014-0390-6

M3 - Article

SN - 1422-6383

VL - 66

SP - 491

EP - 510

JO - Results in Mathematics

JF - Results in Mathematics

IS - 3–4

ER -

On certain Cross varieties of aperiodic monoids with commuting idempotents

Abstract

Bibliographical note

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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