An algebra over a field (simply "algebra" for short) is an algebraic structure consisting of a vector space augmented with a vector multiplication operation obeying suitable axioms. Algebras are well behaved and have notions of dimension, basis, subalgebras, algebra ideals, algebra homomorphisms, and quotient algebras largely analogous to those of vector spaces or rings.\nAlgebras occur often in mathematics, for example the set of all n×n matrices valued in a field k form an algebra M_n(k). We investigate which integers occur as dimensions of subalgebras of M_n(k). We give a description of the dimensions of simple, nilpotent, and semisimple matrix subalgebras along with several sequences that represent various properties of matrix subalgebras.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Heikoop, Phillip Tomas

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042519-100956

Advisor

• Keane, Patrick Gerard

Year

• 2019

Date created

• 2019-04-25

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright