Projects per year

## Abstract

We consider the algebra over a field $K$ with a set of

generators $a_{1},a_{2},\ldots , a_{n}$ and defined by homogeneous

relations of the form

$a_{1}a_{2}\cdots a_{n} =a_{\sigma (1)} a_{\sigma (2)} \cdots a_{\sigma (n)}$,

where $\sigma$ runs through $\Alt_{n}$, the alternating group of

degree $n$. It is shown that for $n=4$ the algebra is

semiprimitive provided $\mbox{char} (K)\neq 2$. If $\mbox{char}

(K)=2$, then it is proved that the Jacobson radical is a finitely

generated ideal that is nilpotent and it is determined by a

congruence on the underlying monoid, defined by the same

presentation. Such a result was proved in an earlier paper for

$n\geq 5$. The proof for $n=4$ is more complicated.

generators $a_{1},a_{2},\ldots , a_{n}$ and defined by homogeneous

relations of the form

$a_{1}a_{2}\cdots a_{n} =a_{\sigma (1)} a_{\sigma (2)} \cdots a_{\sigma (n)}$,

where $\sigma$ runs through $\Alt_{n}$, the alternating group of

degree $n$. It is shown that for $n=4$ the algebra is

semiprimitive provided $\mbox{char} (K)\neq 2$. If $\mbox{char}

(K)=2$, then it is proved that the Jacobson radical is a finitely

generated ideal that is nilpotent and it is determined by a

congruence on the underlying monoid, defined by the same

presentation. Such a result was proved in an earlier paper for

$n\geq 5$. The proof for $n=4$ is more complicated.

Original language | English |
---|---|

Pages (from-to) | 1-26 |

Number of pages | 2009 |

Journal | Contemporary Mathematics |

Publication status | Published - 2010 |

## Keywords

- semigroup ring
- finitely presented
- semigroup
- Jacobson radical
- semiprimitive

## Fingerprint

Dive into the research topics of 'The radical of the four generated algebra of alternating type'. Together they form a unique fingerprint.## Projects

- 4 Finished