## Carl Faith, Ph.D.

### Professor Emeritus, Rutgers University

*Theory of rings and modules*

April 28, 1927 – January 12, 2014

#### Mathematics Genealogy Project

Carl Faith had 9 students and 21 descendants.

**Topics and Areas of Mathematical Work**

(1) The Structure of commutative and non-commutative associative rings(=ring theory) and their modules (= module theory), field theory, theory ofequations, Galois theory for commutative and skew fields, and Ore domains,rings of polynomials, linear and matrix rings, simple, prime or semiprimeGoldie rings, ascending chain conditions on annihilator or irreducible ideals, Noetherian rings and coherent rings. Valuation Theory.

(2) Quotient Rings: maximal and classical quotient rings, especially ringswith self-injective quotient rings.

(3) Quasi-Frobenius (=QF) rings, pseudo-Frobenius (=PF) rings, finitely PF(=FPF) rings.

(4) Decompositions of modules into direct sums, characterizing Noetherian,Artinian, or rings with ascending chain conditions on annihilators. Sigmainjective modules.

(5) Commutativity theorems and the generation of rings by certain elements,e.g., nth powers, or conjugates of certain elements, invariant subrings.

(6) Category theory, especially Abelian categories, and retracts of modulecategories.

(7) History of Twentieth Century Associative Algebra, including mathematicalautobiography (=automathography) and biography (=biomathography)