Rendiconti del Seminario Matematico della Università di Padova

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Volume 135, 2016, pp. 157–173
DOI: 10.4171/RSMUP/135-9

Finitely generated modules and chain rings

Ulrich Albrecht[1] and Gregg Scible[2]

(1) Department of Mathematics, Auburn University, AL 36849-5310, Auburn, USA
(2) Department of Mathematics, Valencia College, P.O. Box 3028, FL 32811, Orlando, USA

This paper investigated finitely generated singular modules over a right chain ring $R$. We show that these modules behave similar to those over valuation rings provided $R$ is a right duo ring. We also demonstrate that the duo condition cannot be removed from our discussion.

Keywords: Chain rings, annihilators, finitely generated, singular module

Albrecht Ulrich, Scible Gregg: Finitely generated modules and chain rings. Rend. Sem. Mat. Univ. Padova 135 (2016), 157-173. doi: 10.4171/RSMUP/135-9