UC San Diego

This thesis is primarily concerned with the behavior of various ring-theoretic properties under base field extension, and in particular with algebras for which such properties are preserved upon extension of scalars. We begin with an investigation of chain conditions on one- sided ideals, and specifically with a new class of rings which we have christened stably noetherian. This is a property which, though fairly natural, has been largely neglected until now. It is a mild enough restriction to encompass many important classes of noncommutative algebras, and yet it is sufficiently restrictive to allow one to prove (or improve upon) theorems of some interest. The first two parts of this thesis make this last statement precise. In the third section we study just infinite rings, which are infinite dimensional algebras for which all homomorphic images are finite dimensional. We prove some new structure-theoretic results, and then investigate the behavior of this property under scalar extension