Characterizations of certain Morita context rings

Abstract

Characterizations of Morita context rings satisfying various additional ring properties, including reflexive, semiprime, prime, NI, weakly 2-primal and 2-primal, are given. The connections between the characterizations of reflexive, semiprime and prime Morita context rings are outlined and shown to be related to torsionless and faithful modules. Similarly, the characterizations of NI, weakly 2-primal and 2-primal are shown to be related. In particular, a characterization of NI Morita context rings is determined to be equivalent to Köthe’s conjecture.

Keywords:

• Morita context ring
• NI
• prime
• reflexive
• semiprime
• weakly 2-primal
• 2-primal

MATHEMATICS SUBJECT CLASSIFICATION:

• 16S99
• 16N40
• 16N60
• 16D90

Acknowledgments

We would like to thank the anonymous referee for carefully reading our manuscript and his comments, which substantially improved the quality and presentation of the paper.