CARL
FAITH
Professor Emeritus,
theory of rings and modules
Rutgers
University
Dept of Mathematics |
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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) |
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