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Ideal intrinsic extensions with connections to PI-rings |
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| Authors: | Efraim P Armendariz Gary F Birkenmeier |
| Institution: | a Department of Mathematics, University of Texas, Austin, TX 78712-1082, USA b Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, USA c Department of Mathematics, Busan National University, Busan 609-735, South Korea |
| Abstract: | In this paper, we extend various classical results by Armendariz and Steinberg, Fisher, Kaplansky, Martindale, Posner, and Rowen on semiprime PI-rings. We do this by introducing several new generalizations of the class of semiprime PI-rings. For these new classes, some structure theorems are obtained, and connections to arbitrary semiprime rings are made (e.g., a semiprime ring has a largest essentially closed ideal from some of these classes). Numerous examples are provided to illustrate and delimit our results. |
| Keywords: | Primary 16N60 16R99 secondary 16R20 16D25 16N99 |
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