Introduction to Regular Rings

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

Chapter 1 in Excursions in Ring Theory, 2026, pp 1-128 from Springer

Abstract: Abstract In this opening chapter, we introduce three of the most basic classes of rings to be studied in this book; namely, the classes of regular rings, unit-regular rings, and strongly regular rings. Throughout our exposition, we will consistently stress an “element-wise" approach to our subject, since such an approach usually gives us a broader and more flexible view of the matter at hand. By definition, a ring element a ϵ R is said to be regular (in the sense of von Neumann [VN2]) if a = axa for some x ϵ R, unit-regular if a = aua for some unit u ϵ R, and strongly regular if a ϵ Ra2 ⋂ a2R.

Date: 2026
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DOI: 10.1007/978-3-032-26301-8_1

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