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Additive Representations of Elements in Rings: A Survey

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Algebra and its Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 174))

Abstract

This article presents a brief survey of the work done on various additive representations of elements in rings. In particular, we study rings where each element is a sum of units; rings where each element is a sum of idempotents; rings where each element is a sum of idempotents and units; and rings where each element is a sum of additive commutators. We have also included a number of open problems in this survey to generate further interest among readers in this topic.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, St. Louis University, St. Louis, MO, 63103, USA

    Ashish K. Srivastava

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  1. Ashish K. Srivastava
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Correspondence to Ashish K. Srivastava .

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Editors and Affiliations

  1. The Ohio State University, Department of Mathematics, The Ohio State University, LIMA, Ohio, USA

    Syed Tariq Rizvi

  2. Aligarh Muslim University, Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Asma Ali

  3. University of Messina, Department of Mathematics & Computer Sci University of Messina, Messina, Italy

    Vincenzo De Filippis

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Srivastava, A.K. (2016). Additive Representations of Elements in Rings: A Survey. In: Rizvi, S., Ali, A., Filippis, V. (eds) Algebra and its Applications. Springer Proceedings in Mathematics & Statistics, vol 174. Springer, Singapore. https://doi.org/10.1007/978-981-10-1651-6_4

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