Finitely Presented Modules over Serial Rings

Gennadi Puninski
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Gennadi Puninski: Moscow State Social University, Department of Mathematics

Chapter Chapter 2 in Serial Rings, 2001, pp 20-33 from Springer

Abstract: Abstract Let P = ⊕ k=1 n e k R, Q = ⊕ l=1 m e l R be finitely generated projective modules over a serial ring R and let f: P → Q be a homomorphism. Since every homomorphism from e k R to e l R is given by left multiplication by an element of R lk , therefore f is induced by left multiplication by an m × n matrix (r ij ), where r ij ∈ R ij . The following lemma shows that this matrix can be diagonalized by choosing appropriate bases for P and Q.

Date: 2001
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DOI: 10.1007/978-94-010-0652-1_2

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