Lee and Zhou introduced the clean index of rings in 2004. Motivated by this work, Basnet and Bhattacharyya introduced both the weak clean index of rings and the nil clean index of rings and Cimpean and Danchev introduced the weakly nil clean index of rings. In this work, we calculate each of these indices for the rings ℤ/nℤ and matrix rings with entries in ℤ/nℤ. A generalized index is also introduced.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Schoonmaker, Benjamin L., "Clean Indices of Common Rings" (2018). All Theses and Dissertations. 7027.
clean rings, clean index, weak clean rings, nil-clean rings, nil clean index