Yıl 2017, Cilt 21, Sayı 21, Sayfalar 180 - 197 2017-01-17
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## WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS

#### Andrada Ciımpean [1] , Peter Danchev [2]

##### 201 216

We introduce and study the weakly nil-clean index associated to a ring. We also give some simple properties of this index and show that rings with the weakly nil-clean index 1 are precisely those rings that are abelian weakly nil-clean, thus showing that they coincide with uniquely weakly nil-clean rings. Next, we define certain types of nilpotent elements and weakly nil-clean decompositions by obtaining some results when the weakly nil-clean index is at most 2 and, moreover, we somewhat characterize rings with weakly nil-clean index 2. After that, we compute the weakly nil-clean index for T2(Zp), T3(Zp) and M2(Z3), respectively, as well as we establish a result on the weakly nilclean index of Mn(R) whenever R is a ring. Our results considerably extend and correct the corresponding ones from [Int. Electron. J. Algebra 15(2014), 145–156]

: Nil-clean ring, uniquely nil-clean ring, weakly nil-clean ring
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Konular Matematik Makaleler Yazar: Andrada Ciımpean Yazar: Peter Danchev
 Bibtex @araştırma makalesi { ieja296326, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {21}, pages = {180 - 197}, doi = {10.24330/ieja.296326}, title = {WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS}, key = {cite}, author = {Danchev, Peter and Ciımpean, Andrada} } APA Ciımpean, A , Danchev, P . (2017). WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS. International Electronic Journal of Algebra, 21 (21), 180-197. DOI: 10.24330/ieja.296326 MLA Ciımpean, A , Danchev, P . "WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS". International Electronic Journal of Algebra 21 (2017): 180-197 Chicago Ciımpean, A , Danchev, P . "WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS". International Electronic Journal of Algebra 21 (2017): 180-197 RIS TY - JOUR T1 - WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS AU - Andrada Ciımpean , Peter Danchev Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.296326 DO - 10.24330/ieja.296326 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 180 EP - 197 VL - 21 IS - 21 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.296326 UR - http://dx.doi.org/10.24330/ieja.296326 Y2 - 2016 ER - EndNote %0 International Electronic Journal of Algebra WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS %A Andrada Ciımpean , Peter Danchev %T WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 21 %N 21 %R doi: 10.24330/ieja.296326 %U 10.24330/ieja.296326 ISNAD Ciımpean, Andrada , Danchev, Peter . "WEAKLY NIL-CLEAN INDEX AND UNIQUELY WEAKLY NIL-CLEAN RINGS". International Electronic Journal of Algebra 21 / 21 (Ocak 2017): 180-197. http://dx.doi.org/10.24330/ieja.296326