Rendiconti del Seminario Matematico della Università di Padova


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Volume 136, 2016, pp. 277–289
DOI: 10.4171/RSMUP/136-18

On the existence of maximal $\mathcal S$-closed submodules

Ulrich Albrecht[1]

(1) Department of Mathematics, Auburn University, AL 36849-5310, Auburn, USA

The goal of this paper is to characterize the right non-singular rings $R$ for which every non-singular right $R$-module contains a maximal $\mathcal S$-closed submodule. Several examples and related results are given.

Keywords: $\mathcal S$-closed submodule, primitive idempotents, reduced ring

Albrecht Ulrich: On the existence of maximal $\mathcal S$-closed submodules. Rend. Sem. Mat. Univ. Padova 136 (2016), 277-289. doi: 10.4171/RSMUP/136-18