Jónsson and HS Modules over Commutative Rings. (12th March 2014) - Oman, Greg
Abstract : LetR be a commutative ring with identity and letM be an infinite unitaryR -module. (Unless indicated otherwise, all rings are commutative with identity 1 ≠ 0 and all modules are unitary.) ThenM is called a Jónsson module provided every proper submodule ofM has smaller cardinality thanM . Dually, M is said to be homomorphically smaller (HS for short) if| M / N | < | M | for every nonzero submoduleN ofM . In this survey paper, we bring the reader up to speed on current research on these structures by presenting the principal results on Jónsson and HS modules. We conclude the paper with several open problems.