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In 2013, Diesl defined a nil clean ring as a ring of which all elements can be expressed as the sum of an idempotent and a nilpotent. Furthermore, in 2017, Y. Zhou, S. Sahinkaya, G. Tang studied nil clean group rings, finding both necessary condition and sufficient condition for a group ring to be a nil clean ring. We have proposed a necessary and sufficient condition for a group ring to be a uniquely nil clean ring. Additionally, we provided theorems for general nil clean group rings, and some examples of trivial-center groups of which group ring is not nil clean over any strongly nil clean rings.
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참고문헌 (10)
참고문헌 신청
J. Chen / 2006 / Morphic group rings / J. Pure Appl. Algebra 205(3):621~639
I. G. Connell / 1963 / On the group ring / Canadian J. Math. 15:650~685
A. J. Diesl / 2013 / Nil clean rings / J. Algebra 383:197~211
T. Kosan / 2016 / Nil-clean and strongly nil-clean rings / J. Pure Appl. Algebra 220(2):633~646
T. Y. Lam / 2001 / A First Course in Noncommutative Rings / Springer-Verlag
I. G. Connell / 1963 / On the group ring / Canadian J. Math. 15:650~685
A. J. Diesl / 2013 / Nil clean rings / J. Algebra 383:197~211
T. Kosan / 2016 / Nil-clean and strongly nil-clean rings / J. Pure Appl. Algebra 220(2):633~646
T. Y. Lam / 2001 / A First Course in Noncommutative Rings / Springer-Verlag
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