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Basic Abstract Algebra by S. K. Jain, S. R. Nagpaul, P. B. Bhattacharya

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CHAPTER 19

Noetherian and artinian modules and rings

1 images

We begin this chapter by proving a result that is quite useful in studying the ring of endomorphisms of a direct sum of modules and that has applications in subsequent sections. Unless otherwise stated, all modules considered in this chapter are left modules.

1.1 Theorem. Let images be a direct sum of R-modules Mi. Then

images

as rings. (The right side is a ring T, say, of k × k matrices ƒ = (ƒij) under ...

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