Minimal spectrum and the radical of Chinese algebras

Ferran Cedó; Jan Okniński

doi:https://doi.org/10.1007/s10468-012-9339-1

Minimal spectrum and the radical of Chinese algebras

Ferran Cedó, Jan Okniński

Department of Mathematics

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

4 Citations (Scopus)

Abstract

It is shown that every minimal prime ideal of the Chinese algebra of any finite rank is generated by a finite set of homogeneous elements of degree 2 or 3. A constructive way of producing minimal generating sets of all such ideals is found. As a consequence, it is shown that the Jacobson radical of the Chinese algebra is nilpotent. Moreover, the radical is not finitely generated if the rank of the algebra exceeds 2. © 2012 Springer Science+Business Media B.V.

Original language	English
Pages (from-to)	905-930
Journal	Algebras and Representation Theory
Volume	16
DOIs	https://doi.org/10.1007/s10468-012-9339-1
Publication status	Published - 1 Aug 2013

Keywords

Chinese algebra
Finitely presented
Jacobson radical
Minimal prime ideal
Nilpotent radical
Semigroup ring

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AU - Cedó, Ferran

AU - Okniński, Jan

PY - 2013/8/1

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N2 - It is shown that every minimal prime ideal of the Chinese algebra of any finite rank is generated by a finite set of homogeneous elements of degree 2 or 3. A constructive way of producing minimal generating sets of all such ideals is found. As a consequence, it is shown that the Jacobson radical of the Chinese algebra is nilpotent. Moreover, the radical is not finitely generated if the rank of the algebra exceeds 2. © 2012 Springer Science+Business Media B.V.

AB - It is shown that every minimal prime ideal of the Chinese algebra of any finite rank is generated by a finite set of homogeneous elements of degree 2 or 3. A constructive way of producing minimal generating sets of all such ideals is found. As a consequence, it is shown that the Jacobson radical of the Chinese algebra is nilpotent. Moreover, the radical is not finitely generated if the rank of the algebra exceeds 2. © 2012 Springer Science+Business Media B.V.

KW - Chinese algebra

KW - Finitely presented

KW - Jacobson radical

KW - Minimal prime ideal

KW - Nilpotent radical

KW - Semigroup ring

U2 - https://doi.org/10.1007/s10468-012-9339-1

DO - https://doi.org/10.1007/s10468-012-9339-1

M3 - Article

VL - 16

SP - 905

EP - 930

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

ER -