Commutative neat group rings |
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| Authors: | D Udar R K Sharma J B Srivastava |
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| Institution: | 1. Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi, Indiadineshudar@yahoo.com;3. Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi, India |
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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 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. |
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| Keywords: | Clean rings group rings neat rings semiclean rings |
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