JP Journal of Algebra, Number Theory and Applications
Volume 38, Issue 3, Pages 213 - 225
(June 2016) http://dx.doi.org/10.17654/NT038030213 |
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ON NICE MODULES
A. Ismarwati, H. France-Jackson, Sri Wahyuni and I. E. Wijayanti
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Abstract: A ring with identity is called a clean ring if every element of the ring decomposes as a sum of an idempotent and a unit of the ring.
Trying to answer an open question put on by W. K. Nicholson, we introduce and investigate the new concept of a nice module, that is a module whose every submodule has a clean endomorphism ring. We present some sufficient conditions under which a module is nice, give examples of module that are nice and those that are not nice, show how to construct nice modules and raise an interesting question in the meantime. |
Keywords and phrases: clean module, automorphism invariant module, module of finite length. |
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