#### Campus Units

Mathematics

#### Document Type

Article

#### Publication Date

2008

#### Journal or Book Title

Experimental Mathematics

#### Volume

17

#### Issue

2

#### First Page

245

#### Last Page

255

#### 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.

#### Copyright Owner

Taylor & Francis

#### Copyright Date

2008

#### Language

en

#### File Format

application/pdf

#### Recommended Citation

Hentzel, Irvin R. and Peresi, L. A., "Nuclear Elements of Degree 6 in the Free Alternative Algebra" (2008). *Mathematics Publications*. 143.

https://lib.dr.iastate.edu/math_pubs/143

## Comments

This article is published as Hentzel, I. R., and L. A. Peresi. "Nuclear Elements of Degree 6 in the Free Alternative Algebra."

Experimental Mathematics17, no. 2 (2008): 245-255. Posted with permission.