Jónsson Modules over Commutative Rings
نویسنده
چکیده
Let M be an infinite unitary module over a commutative ring R with identity. Then M is called a Jónsson module provided every proper submodule of M has smaller cardinality than M. These modules have been studied by several algebraists, including Robert Gilmer, Bill Heinzer, and the author. In this note, we recall the major results on Jónsson modules to bring the reader up to speed on current research. Included are some applications to Artinian and uniserial modules as well as quasi-cyclic groups. There are several wide open problems in this area, some of which may be independent of the usual axioms of set theory. We close the article with a discussion of several such problems and outline some possible strategies for solving them. 2000 AMS Subject Classification: 13C99, 03E10. All rings in this paper are assumed to be commutative with identity, and all modules are assumed to be unitary.
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