Presimplifiable and Cyclic Group Rings |
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| Authors: | Manal Ghanem Alun Wyn-Jones Hassan Al-Ezeh |
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| Institution: | 1. Department of Mathematics , Irbid National University , Amman , Jordan dr_mghanem@yahoo.com;3. Mathematical Models, Inc. , New York , USA;4. Department of Mathematics , Jordan University , Amman , Jordan |
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| Abstract: | Let R be any commutative ring with identity, and let C be a (finite or infinite) cyclic group. We show that the group ring R(C) is presimplifiable if and only if its augmentation ideal I(C) is presimplifiable. We conjecture that the group rings R(C n ) are presimplifiable if and only if n = p m , p ∈ J(R), p is prime, and R is presimplifiable. We show the necessity of n = p m , and we prove the sufficiency when n = 2, 3, 4. These results were made possible by a new formula derived herein for the circulant determinantal coefficients. |
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| Keywords: | Augmentation ideal Circulant determinant Group ring Presimplifiable ring |
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