## Experimental Mathematics

- Experiment. Math.
- Volume 17, Issue 2 (2008), 245-255.

### Nuclear Elements of Degree 6 in the Free Alternative Algebra

I. R. Hentzel and L. A. Peresi

#### Abstract

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known degree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

#### Article information

**Source**

Experiment. Math., Volume 17, Issue 2 (2008), 245-255.

**Dates**

First available in Project Euclid: 19 November 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1227118975

**Mathematical Reviews number (MathSciNet)**

MR2433889

**Zentralblatt MATH identifier**

1208.17024

**Subjects**

Primary: 17D05: Alternative rings

Secondary: 17-04: Explicit machine computation and programs (not the theory of computation or programming) 17-08: Computational methods 68W30: Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]

**Keywords**

Free alternative algebras nucleus polynomial identities computational algebra

#### Citation

Hentzel, I. R.; Peresi, L. A. Nuclear Elements of Degree 6 in the Free Alternative Algebra. Experiment. Math. 17 (2008), no. 2, 245--255. https://projecteuclid.org/euclid.em/1227118975