Construction of a two unique product semigroup defined by permutation relations of quaternion type

Ferran Cedó; Eric Jespers; Georg Klein

doi:10.1016/j.jalgebra.2015.12.017

Construction of a two unique product semigroup defined by permutation relations of quaternion type

Ferran Cedó, Eric Jespers, Georg Klein

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Abstract

© 2016 Elsevier Inc.. For a regular representation H⊆Symn of the generalized quaternion group of order n=4k, with k≥2, the monoid Sn(H) presented with generators a1, a2, . . ., an and with relations a1a2⋯an=aσ(1)aσ(2)⋯aσ(n), for all σ∈H, is investigated. It is shown that Sn(H) has the two unique product property. As a consequence, for any field K, the monoid algebra K[Sn(H)] is a domain with trivial units which is semiprimitive.

Original language	English
Pages (from-to)	196-211
Journal	Journal of Algebra
Volume	452
DOIs	https://doi.org/10.1016/j.jalgebra.2015.12.017
Publication status	Published - 15 Apr 2016

Keywords

Finitely presented
Jacobson radical
Semigroup algebra
Semigroup ring
Semiprimitive
Symmetric presentation
Unique product

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10.1016/j.jalgebra.2015.12.017

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title = "Construction of a two unique product semigroup defined by permutation relations of quaternion type",

abstract = "{\textcopyright} 2016 Elsevier Inc.. For a regular representation H⊆Symn of the generalized quaternion group of order n=4k, with k≥2, the monoid Sn(H) presented with generators a1, a2, . . ., an and with relations a1a2⋯an=aσ(1)aσ(2)⋯aσ(n), for all σ∈H, is investigated. It is shown that Sn(H) has the two unique product property. As a consequence, for any field K, the monoid algebra K[Sn(H)] is a domain with trivial units which is semiprimitive.",

keywords = "Finitely presented, Jacobson radical, Semigroup algebra, Semigroup ring, Semiprimitive, Symmetric presentation, Unique product",

author = "Ferran Ced{\'o} and Eric Jespers and Georg Klein",

year = "2016",

month = apr,

day = "15",

doi = "10.1016/j.jalgebra.2015.12.017",

language = "English",

volume = "452",

pages = "196--211",

journal = "Journal of Algebra",

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T1 - Construction of a two unique product semigroup defined by permutation relations of quaternion type

AU - Cedó, Ferran

AU - Jespers, Eric

AU - Klein, Georg

PY - 2016/4/15

Y1 - 2016/4/15

N2 - © 2016 Elsevier Inc.. For a regular representation H⊆Symn of the generalized quaternion group of order n=4k, with k≥2, the monoid Sn(H) presented with generators a1, a2, . . ., an and with relations a1a2⋯an=aσ(1)aσ(2)⋯aσ(n), for all σ∈H, is investigated. It is shown that Sn(H) has the two unique product property. As a consequence, for any field K, the monoid algebra K[Sn(H)] is a domain with trivial units which is semiprimitive.

AB - © 2016 Elsevier Inc.. For a regular representation H⊆Symn of the generalized quaternion group of order n=4k, with k≥2, the monoid Sn(H) presented with generators a1, a2, . . ., an and with relations a1a2⋯an=aσ(1)aσ(2)⋯aσ(n), for all σ∈H, is investigated. It is shown that Sn(H) has the two unique product property. As a consequence, for any field K, the monoid algebra K[Sn(H)] is a domain with trivial units which is semiprimitive.

KW - Finitely presented

KW - Jacobson radical

KW - Semigroup algebra

KW - Semigroup ring

KW - Semiprimitive

KW - Symmetric presentation

KW - Unique product

U2 - 10.1016/j.jalgebra.2015.12.017

DO - 10.1016/j.jalgebra.2015.12.017

M3 - Article

VL - 452

SP - 196

EP - 211

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

Construction of a two unique product semigroup defined by permutation relations of quaternion type

Abstract

Keywords

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