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ABSTRACT A ring R is called clean if every element of it is a sum of an idempotent and a unit. A ring R is neat if every proper homomorphic… Click to show full abstract
ABSTRACT A ring R is called clean if every element of it is a sum of an idempotent and a unit. A ring R is neat if every proper homomorphic image of R is clean. When R is a field, then a complete characterization has been obtained for a commutative group ring RG to be neat, but not clean. And if R is not a field, then necessary conditions are obtained for a commutative group ring RG to be neat, but not clean. A counterexample is given to show that these necessary conditions are not sufficient.
Keywords:
neat group;
commutative neat;
group;
group rings;
ring neat
Journal Title: Communications in Algebra
Year Published: 2017
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Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!