Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599597 | Linear Algebra and its Applications | 2014 | 20 Pages |
Abstract
If D is an integral domain in which every element can be factored as a product of irreducible elements, then every element A∈Tn(D)A∈Tn(D), the semigroup of upper triangular matrices with nonzero determinant, can be factored as a product of irreducible elements. We classify both the irreducible elements and units of this cancellative semigroup. Having achieved this, we provide a means of measuring the uniqueness or non-uniqueness of these factorizations in terms of the uniqueness or non-uniqueness of factorizations in D. In addition to using well-studied invariants from factorization theory of commutative semigroups, we introduce a new tool, weak transfer homomorphisms, which are more appropriate for noncommutative settings.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dale Bachman, Nicholas R. Baeth, James Gossell,