Fitting Theory and Modules Over Regular Rings

T. Y. Lam ()
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T. Y. Lam: University of California, Berkeley, Department of Mathematics

Chapter 2 in Excursions in Ring Theory, 2026, pp 129-205 from Springer

Abstract: Abstract In the beginning section of this Chapter, we introduce the all-important notion of a Fitting decomposition of a module with an operator, and show how this notion leads naturally to the notion of a strongly π-regular element in a ring, in generalization of the notion of a strongly regular element de ned in §3. This paves the way to the introduction of two new classes of rings; namely, π -regular rings, and strongly π -regular rings. The basic theory of these two classes of rings, including full proofs of Azumaya's lemma, Dischinger's theorem, several Fisher-Snider theorems, and a theorem of Goodearl and Menal, is developed in §§4-5.

Date: 2026
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DOI: 10.1007/978-3-032-26301-8_2

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